t 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


GIFT  OF 

Dr.  William  H.  Ivie 


THE  GASOLINE  AUTOMOBILE 

Its  Design  and  Construction 


VOLUME  II 


Transmission,   Running 
Gear  and  Control 


By 

P.  M.  HELDT 
Technical  Editor  of  The  Horseless  Age 


Second  Edition 


P.  M.  HELDT 

Nyack,  N.  Y. 

1917 


Copyrighted  by 
P.  M.  HELDT 

1917 
Previous  Copyright,  1913. 


GUT 

"T  vA 


(ALL  RIGHTS  RESERVED) 


PREFACE. 

DURING  the  period  that  intervened  between  the  original  writ- 
ing of  this  volume  and  the  present  revision,  a  number  of 
notable  evolutions  took  place  in  the  design  of  some  of  the 
component  parts  which  are  dealt  with  here.  The  most  important 
of  these  was  undoubtedly  the  introduction  of  the  helical  bevel 
gear  drive.  The  adoption,  of  this  drive  confronted  automobile 
engineers  with  new  problems,  chiefly  in  regard  to  bearing  loads; 
these  are  discussed  in  some  detail  in  the  present  edition  and  rules 
for  the  calculation  of  the  bearing  loads  are  given. 

While  the  bevel-spur  and  the  internal  gear  drive  were  both  in 
use  at  the  time  the.  first  edition  was  prepared,  only  a  single  firm 
was  prominently  identified  with  each  in  the  United  States,  so 
they  were  not  deemed  of  sufficinent  importance  to  warrant  special 
treatment.  Since  then,  however,  the  internal  gear  drive  has  made 
notable  progress  in  this  country  and  the  bevel-spur  drive  has 
assumed  some  importance  in  England.  At  the  same  time  addi- 
tional interest  has  been  aroused  in  the  four  wheel  drive  for  mili- 
tary and  similar  trucks,  so  it  was  decided  to  add  a  chapter  cover- 
ing these  three  forms  of  final  drive. 

The  advent  of  the  high  speed  motor,  together  with  a  great  in- 
crease in  the  use  of  unit  power  plants,  resulting  in  the  lengthening 
of  propeller  shafts,  has  compelled  designers  to  give  more  atten- 
tion to  the  problem  of  critical  speeds  in  shafts.  Some  matter  on 
this  subject  has  been  incorporated  in  the  Chapter  on  The  Bevel 
Gear  Drive  and  Rear  Axle,  the  theory  of  critical  speeds  being 
explained  and  rules  for  their  calculation  given. 

Another  branch  of  automobile  engineering  in  which  great  com- 
mercial development  has  taken  place  during  the  past  four  years 
is  that  relating  to  the  worm  drive.  The  chapter  devoted  to  this 
subject  has  been  largely  rewritten  and  brought  up  to  date.  Minor 
additions  and  changes  have  been  made  throughout  the  book,  and 
a  number  of  typographical  and  other  errors  that  occurred  in  the 
first  edition  have  been  corrected.  For  pointing  out  such  errors 
the  author  wishes  to  thank  some  of  his  readers. 


M80S109 


PREFACE. 

It  may  appear  that  in  the  chapters  on  the  Sliding  Change  Gear 
and  on  Rear  Axles,  the  annular  ball  bearing  receives  more  atten- 
tion than  is  warranted  by  the  scale  of  its  present  day  use.  Owing 
— at  least  in  part — to  the  interruption  of  imports  of  ball  bearings 
from  Europe,  roller  bearings  now  predominate  largely  in  auto- 
mobile construction.  The  problems  of  mounting,  however,  are 
very  much  the  same  as  with  ball  bearings,  and  numerous  examples 
of  mounting  roller  bearings  are  given  in  the  plates  at  the  end  of 
the  book  as  well  as  in 'the  text  illustrations.  In  the  most  expen- 
sive cars  the  annular  ball  bearing  still  retains  a  prominent  place, 
and  it  was,  therefore,  not  deemed  necessary  to  rewrite  this  part  of 
the  work. 

As  nearly  all  of  the  old  plates  had  to  be  discarded  it  was  de- 
cided to  incorporate  the  plates  in  the  book  itself.  Chassis  views 
are  shown  for  the  most  part  in  half  tone,  so  the  line  cuts  show 
only  chassis  components  and  these  can  be  presented  on  a  suffi- 
ciently large  scale  on  a  5j4x8j4  sheet. 

THE  AUTHOR. 


LIST  OF  CHAPTERS 


CHAPTER  I. 
GENERAL  LAYOUT  OF  CARS 3 

CHAPTER  II. 
FRICTION   CLUTCHES    13 

CHAPTER  III. 
SLIDING  CHANGE  SPEED  GEARS 70 

CHAPTER  IV. 
PLANETARY  CHANGE  SPEED  GEARS 125 

CHAPTER  V. 
FRICTION  Disc  DRIVE   147 

CHAPTER  VI. 
UNIVERSAL  JOINTS    160 

CHAPTER  VII. 
DIFFERENTIAL   GEARS    180 

CHAPTER  VIII. 
UNIT  POWER  PLANTS,  TRANSMISSION  AXLES 193 

CHAPTER  IX. 
BEVEL  GEAR  DRIVE  AND  REAR  AXLE ; 203 

CHAPTER  X. 
THE  WORM  GEAR  DRIVE 293 

CHAPTER  XI. 
THE  CHAIN  DRIVE 323 

CHAPTER  XII. 
BEVEL-SPUR  GEAR,  INTERNAL  GEAR  AND  FOUR  WHEEL  DRIVES.    341 

CHAPTER  XIII. 
BRAKES 357 

CHAPTER  XIV. 
FRONT  AXLES 386 

CHAPTER  XV. 
STEERING  GEARS 411 

CHAPTER  XVI. 
CONTROL    441 

CHAPTER  XVII. 

FRAMES    471 

CHAPTER  XVIII. 
SPRINGS  .  497 


CHAPTER  XIX. 


ROAD  WHEELS  528 

APPENDIX 543 

PLATES    , 571 


LIST  OF  PLATES. 


CHANGE  SPEED  GEAR  OF  THE  PACKARD  TWELVE 571 

DRY  Disc  CLUTCH  OF  CHALMERS  6-30 572 

BROWN-LIPE  DRY  Disc  CLUTCH  ON  CUNNINGHAM  CAR 573 

MARMON  CONE  CLUTCH 574 

SIMPLEX  LUBRICATED  Disc  CLUTCH 575 

MUNCIE  CLUTCH  AND  CHANGE  GEAR 576 

CASE  CLUTCH  AND  CHANGE  GEAR 577 

BORG  &  BECK  PLATE  CLUTCH  AND  COVERT  CHANGE  GEAR 578 

TIMKEN  TRUCK  FRONT  AXLE  (7200  LBS.  MAX.  LOAD) 579 

"AMERICAN"  PLEASURE  CAR  REAR  AXLE 580 

TIMKEN  PLEASURE  CAR  REAR  AXLE 581 

TIMKEN  WORM  DRIVE  TRUCK  REAR  AXLE 582 

TORBENSEN  INTERNAL  GEAR  DRIVE  TRUCK  AXLE 583 

Two  FRENCH  INTERNAL  GEAR  TRUCK  DRIVES 584 

'AMERICAN"  PLEASURE  CAR  FRONT  AXLE 585 

FRANKLIN  STEERING  GEAR 586 

BENZ  STEERING  GEAR 587 

PEERLESS  TRUCK  STEERING  GEAR 588 

SPICER  PROPELLER  SHAFT  ASSEMBLY 589 

FRANKLIN  THROTTLE  CONTROL  ASSEMBLY 589 

PLAN  VIEW  OF  LIPPARD- STEWART  1000  LB.  TRUCK  CHASSIS  590 
SIDE  ELEVATION  OF  LIPPARD-STEWART  1000  LB.  TRUCK 

CHASSIS  591 

WINTON  SPARK  AND  THROTTLE  CONTROL  (ABOVE)  AND 

CLUTCH  AND  BRAKE  CONTROL  (BELOW) 592 

PLAN  VIEW  OF  INTERSTATE  FOUR  CYLINDER  CHASSIS 593 

LEXINGTON-HOWARD  Six  CYLINDER  CHASSIS 594 

PLAN  VIEW  OF  LEXINGTON-HOWARD  CHASSIS 595 

CADILLAC  EIGHT  CYLINDER  CHASSIS  MODEL  55 596 

PLAN  VIEW  OF  CADILLAC  EIGHT  CYLINDER  CHASSIS 597 

PACKARD  FIVE  TON  TRUCK  CHASSIS 598 

PLAN  VIEW  OF  PACKARD  FIVE  TON  TRUCK  CHASSIS 599 

PLAN  VIEW  OF  STUDEBAKER  FOUR  CYLINDER  CHASSIS 600 

PLAN  VIEW  OF  AUBURN  FOUR  CYLINDER  CHASSIS 601 

PLAN  VIEW  OF  HUDSON  SUPER- Six  CHASSIS..  602 


CHAPTER  I. 


GENERAL  STRUCTURE  OF  THE  CAR. 

Location  of  Motor — In  the  first  attempts  to  build  road 
vehicles  propelled  by  gasoline  motors  the  general  lines  of 
horse  vehicles  were  followed.  The  latter  were  then  regarded 
as  the  highest  type  of  vehicular  design,  and  any  departure 
from  their  lines  was  thought  to  be  undesirable,  as  it  offended 
the  eye.  This  made  it  necessary  to  place  the  power  plant 
under  the  body,  and  considerable  difficulty  was  often  experi- 
enced in  getting  it  into  this  cramped  space.  It  was  thought 
essential  to  conceal  the  mechanical  part  of  the  vehicle  as 
much  as  possible,  because  what  people  wanted  was  a  self- 
moving  carriage  and  not  a  road  locomotive  or  a  machine  akin 
thereto.  Before  long,  however,  some  bold  spirit  stood  up  for 
the  idea  that  the  pov/cr  plant  deserved  such  a  location  on  the 
vehicle  that  it  could  be  designed  without  regard  to  the  space 
available  in  the  body,  and  that  when  it  required  attention  it 
zould  be  reached  quickly  and  without  disturbing  the  passen- 
gers. The  precedent  then  set  has  since  been  generally  fol- 
lowed, and  with  very  few  exceptions  the  motor  is  now  located 
at  the  front  of  the  car  under  a  bonnet.  It  is  hardly  neces- 
sary to  add  that  the  public's  conception  of  what  a  motor  ve- 
hicle should  look  like  has  greatly  changed  since  then. 

Spring  Suspension  of  Power  Plant — The  early  automo- 
biles built  in  this  country,  almost  without  exception,  had  reach 
rods  or  perches  extending  between  the  front  and  rear  axles, 
the  object  of  which  was  to  free  the  body  springs  of  the  driv- 
ing thrust.  Some  designers  then  placed  the  power  plant  on 
these  reaches,  so  as  to  simplify  the  problem  of  transmission 
to  the  wheels.  It  was  soon  recognized,  however,  that,  even 
though  pneumatic  tires  were  used,  the  vibration  was  so  strong 
that  it  was  practically  impossible  to  keep  the  motor  intact. 
Moreover,  the  hammering  effect  of  the  heavy  unsprung  weight 

3 


4  GENERAL  STRUCTURE  OF  CAR. 

on  the  axles,  wheels  and  tires  greatly  reduced  the  life  of  these 
parts.  The  principle  was  thus  established  that  as  much  as 
possible  of  the  weight  of  the  car  should  be  supported  on 
springs,  and  above  all  the  more  delicate  parts,  such  as  the 
motor. 

Number  of  Wheels — The  great  majority  of  all  automobiles 
have  four  wheels.  This  is  the  minimum  number  which  in- 
sures stability  under  all  reasonable  conditions.  Howevei 
cars  have  been  and  are  being  built  with  as  few  as  three  and 
as  many  as  eight  wheels.  The  smaller  number  of  wheels  is 
used  to  reduce  the  manufacturing  cost  of  small  vehicles,  while 
the  larger  numbers,  above  four,  are  used  either  to  keep  the 
load  per  wheel  inside  a  certain  maximum  (as  required  by  the 
road  laws  in  some  countries)  or  to  insure  greater  comfort  of 
riding.  However,  certainly  more  than  99  per  cent,  of  all  auto- 
mobiles (not  including  motorcycles)  are  of  the  four  wheeled 
type,  and  this  construction  may  be  considered  standard. 

Steering  and  Driving — With  the  number  of  wheels  decided 
upon,  the  question  arises  as  to  how  many  and  which  shall  be 
used  for  steering,  and  how  many  and  which  shall  be  used  for 
driving.  With  a  four  wheeled  vehicle  it  is  possible  to  steer 
with  either  the  front  wheels,  the  rear  wheels  or  all  four 
wheels,  and  to  propel  the  vehicle  by  either  one  front  wheel, 
one  rear  wheel,  both  front  wheels,  both  rear  wheels  or  all 
four  wheels.  In  this  connection  it  must  be  borne  in  mind 
that  the  effectiveness  of  both  steering  and  driving  depends 
upon  the  adherence — the  resistance  to  slippage — between  the 
wheels  and  the  ground,  which  in  turn  depends  upon  the 
weight  carried  by  the  wheels.  As  far  as  steering  is  con- 
cerned, at  least  two  wheels  have  to  be  used  for  it  in  a  four 
wheeled  vehicle,  and  if  one-third  or  more  of  the  total  load  is 
carried  on  these  wheels,  then  the  requirement  of  positive 
steering  is  met  in  a  satisfactory  degree.  As  regards  the 
choice  between  the  front  and  rear  wheels  for  steering  pur- 
poses, the  front  wheels  possess  one  important  advantage  over 
the  rear  wheels,  and  tha*  is  that,  if  a  car  stands  alongside 
of  a  curb  or  other  barrier,  and  it  is  desired  to  drive  away 
from  it,  with  rear  steering  this  can  only  be  done  by  back- 
ing up,  because  in  order  to  cause  the  car  to  turn  away  from 
it  in  driving  forward,  the  steering  wheels  would  have  to  be 
turned  toward  the  curb  and  would  run  into  it.  Rear  steer- 
ing was  used  fcr  many  years  on  electric  cabs  in  New  York 
City,  but  the  disadvantage  mentioned  is  greatly  against  it, 


GENERAL  STRUCTURE  OF  CAR.  5 

and  has  been  one  of  the  points  that  led  to  its  abandon- 
ment. The  only  advantage  of  four  wheel  steering  would  be 
that  with  a  certain  maximum  deflection  or  "lock"  of  the 
steering  wheels,  a  car  with  four  wheel  steering  could  turn 
in  a  much  smaller  radius  than  one  with  two  wheel  steering. 
Four  wheel  steering,  however,  would  be  subject  to  the  disad- 
vantage of  rear  wheel  steering  referred  to  in  the  foregoing, 
and  the  further  disadvantage  of  the  complication  involved  in 
combined  driving  and  steering  wheels,  which  more  than  offset 
its  slight  advantage,  and  it  is  therefore  never  used. 

As  regards  the  number  of  driving  wheels,  it  would  greatly 
simplify  the  problem  of  transmitting  the  power  from  the 
motor  to  its  point  of  application  if  only  a  single  wheel  was 
used  for  driving.  The  simplification  which  results  from  this 
arrangement,  as  compared  with  that  in  which  two  wheels  are 
used  for  driving,  is  one  of  the  main  considerations  which  lead 
to  the  selection  of  three  wheeled  construction  in  certain  in- 
stances. However,  in  order  that  a  vehicle  may  have  plenty 
of  traction  or  road  adherence  under  all  conditions,  even  on 
steep  grades  with  greasy  road  surface,  at  least  50  per  cent, 
of  the  total  weight  to  be  propelled  must  be  carried  on  the 
driving  wheel  or  wheels.  Besides,  in  the  ordinary  four 
wheeled  vehicle,  if  power  was  applied  to  one  wheel — in  other 
words,  at  one  side  only — it  would  tend  to  cause  the  car  to 
slew  or  skid  easily  and  affect  the  steering  unfavorably.  Driv- 
ing through  at  least  two  wheels  is  therefore  considered  essen- 
tial to  successful  operation.  As  to  whether  the  front  or  the 
rear  wheels  should  be  driven,  one  thing  that  is  largely  deter- 
mining in  this  matter  is  that  the  front  wheels  are  used  for 
steering,  and  it  involves  considerable  mechanical  complica- 
tion to  use  the  same  wheels  for  both  driving  and  steering. 
Moreover,  if  the  motor  is  located  at  the  front  end  of  the  car 
it  can  more  easily  be  placed  in  driving  connection  with  the 
rear  wheels  than  with  the  front  wheels.  It  must  be  remem- 
bered that  the  motor  is  carried  upon  a  spring  supported 
frame,  and  therefore  constantly  changes  its  position  with  rela- 
tion'to  the  axles;  this  relative  change  in  position  must  be 
allowed  for  by  some  form  of  flexible  connection,  and  this  can 
be  done  more  easily  if  the  motor  is  at  a  considerable  distance 
horizontally  from  the  axle  to  which  it  is  connected  in  driv- 
ing relation.  There  are  several  real  advantages  in  front  driv- 
ing. Owing  to  the  fact  that  the  propelling  force  acts  at  a 
tangent  to  the  circumference  of  the  driving  wheels,  if  the 


6  GENERAL  STRUCTURE  OF  CAR. 

front  wheels  are  drivers,  and  they  drop  into  a  mud  puddle, 
for  instance,  they  tend  to  climb  out  of  it,  as  it  were,  while 
with  rear  drive  the  combined  effect  of  the  forward  thrust  of 
the  rear  wheels  and  the  weight  on  the  front  wheels  may  force 
the  latter  deeper  into  the  mud.  Another  advantage  of  front 
driving  is  that  with  it  there  is  much  less  tendency  to  skid 
than  with  rear  driving.  The  problem  of  driving  through  the 
steering  wheels  can,  of  course,  be  solved,  but  it  involves  the 
use  of  two  universal  joints,  preferably  of  a  type  which  insures 
uniform  transmission  of  motion  irrespective  of  the  angle  be- 
tween the  connected  shafts,  which  must  be  so  placed  that  the 
point  of  intersection  of  the  two  connected  shafts  lies  in  the 
centre  line  of  the  steering  knuckle  pin. 

Four  Wheel  Drive — Driving  on  all  four  wheels  has  been 
employed  to  some  extent,  particularly  on  army  wagons,  which 
may  under  conditions  have  to  travel  off  the  roads.  Four 
wheel  driving  makes  the  whole  weight  of  the  vehicle  and  load 
available  for  traction  purposes,  which  is  an  advantage  when 
the  streets  are  covered  with  ice  or  snow,  or  for  some  other 
reason  are  exceedingly  slippery.  This  system  of  driving 
would  become  more  important  if  steel  tires  should  ever  come 
into  common  use  for  commercial  vehicles,  since  the  adherence 
between  steel  and  the  different  road  surfaces  is  very  much  less 
than  that  between  rubber  and  these  road  surfaces.  Where  rub- 
ber tires  are  used  sufficient  traction  is  obtained  under  all  nor- 
mal conditions  by  so  arranging  the  design  that  from  one-half 
to  two-thirds  of  the  weight  of  the  car  and  load  is  always  car- 
ried on  the  driving  wheels,  while  under  abnormal  conditions 
such  traction  devices  as  tire  chains  or  steel  studded  tire  covers 
are  resorted  to. 

Thus,  while  the  front  drive  and  four  wheel  drive  are  being 
exploited  to  some  extent,  at  least  99  per  cent,  of  all  automo- 
biles built  are  steered  by  their  front  wheels  and  driven  by  their 
rear  wheels. 

Differential  Gear — If  both  driving  wheels  were  positively 
connected  to  the  single  source  of  motive  power,  they  could  not 
rotate  at  unequal  speeds,  as  is  required  in  turning  corners.  If 
the  wheels  had  to  drive  the  car  forward  only,  the  problem 
could  be  solved  by  driving  them  through  ratchet  clutches,  but 
since  they  must  drive  the  car  backward  as  well  as  forward, 
it  is  necessary  to  incorporate  a  so-called  differential  gear  in 
the  drive  through  which  the  driving  torque  is  always  equally 
divided  between  the  two  driving  wheels,  in  driving  both  for- 


GENERAL    STRUCTURE   OF   CAR  7 

ward  and  backward,  and  which  allows  the  two  wheels  to  turn 
at  different  speeds  as  required  by  the  course  followed,  or  by 
any  slight  difference  in  their  diameters.  With  the  four  wheel 
drive  it  is  necessary  to  use  three  differential  gears,  one  be- 
tween the  front  and  rear  axles  and  one  between  the  two 
wheels  on  each  axle. 

Friction  Clutch— Owing  to  the  fact  that  the  gasoline  motor, 
unlike  steam  and  electric  motors,  does  not  start  from  a  stand- 
still with  full  torque,  but  must  be  started  either  by  means  of  a 
hand  crank  or  some  starting  device  which  generally  produces 
only  sufficient  torque  to  just  turn  the  motor  over  against  the 
compression,  it  is  necessary  to  disconnect  the  motor  from  the 
driving  parts  of  the  vehicle  for  starting  it,  and  after  the  motor 
has  attained  speed,  to  connect  it  to  the  vehicle  again.  For  this 
purpose  a  device  must  be  used  which  will  allow  of  a  certain 
amount  of  slippage,  until  the  motor  speed  has  been  reduced 
and  the  vehicle  speed  increased  to  such  a  point  that  the  two 
correspond.  This  is  accomplished  by  means  of  a  friction 
clutch,  which  is  always  placed  close  to  the  engine  and  gen- 
erally built  together  with  the  flywheel — except  in  those  cars 
provided  with  frictional  means  of  power  transmission,  such  as 
belts,  friction  pulleys  and  friction  discs,  which  latter  devices 
serve  the  dual  purpose  of  changing  the  gear  ratio  between  the 
engine  crankshaft  and  the  road  wheels  and  of  disconnecting 
the  former  from  the  latter. 

Change  Speed  Gear — With  any  but  the  very  lightest  of 
gasoline  motor  vehicles  it  is  necessary  to  provide  means  for 
connecting  the  motor  to  the  driving  wheels  in  several  different 
ratios.  The  gasoline  motor  differs  from  other  light  motors 
in  that  when  running  at  its  speed  of  maximum  economy  or 
its  speed  of  maximum  output,  it  produces  nearly  the  maximum 
torque  of  which  it  is  capable.  The  motor,  of  course,  must  be 
so  geared  that  under  normal  conditions  of  operation — that  is, 
when  the  car  is  traveling  over  a  level  road  at  a  good  speed — it 
runs  at  about  its  speed  of  maximum  economy,  and  it  is  then 
impossible  for  the  motor  to  provide  the  propelling  effort  re- 
quire'd  in  climbing  steep  hills  or  in  passing  through  deep  sand, 
through  the  same  gear  reduction.  It  is,  of  course,  understood 
that  when  two  shafts  or  other  rotating  machine  parts  are  con- 
nected together  in  driving  relation,  the  torques  of  the  two  bear 
to  each  other  the  inverse  ratio  of  their  respective  speeds.  Thus, 
by  providing  a  hill  climbing  gear  giving  a  speed  reduction, 
say,  four  times  as  great  as  the  normal  speed  reduction,  the 


8  GENERAL  STRUCTURE  OF  CAR 

driving  effort  at  the  road  wheel  rims  can  be  quadrupled  for  hill 
climbing.  But  since  the  hill  climbing  or  low  gear  gives  a  com- 
paratively low  vehicle  speed,  it  is  customary  in  all  but  the 
lightest  vehicles  to  provide  either  one  or  two  intermediate 
gears,  for  use  on  moderate  hills,  on  soft  or  uneven  roads,  etc. 
The  change  gear  mechanism,  therefore,  provides  either  three 
or  four  forward  gear  ratios  as  a  general  thing,  and  also  one  re- 
verse gear  ratio.  In  this  country  gear  boxes  with  three  forward 
speeds  are  considerably  more  common,  while  in  Europe  the  four 
speed  gear  is  the  most  popular,  the  difference  being  no  doubt  due 
to  the  fact  that  we  employ  relatively  more  powerful  motors. 

Single  and  Double  Reduction  —  There  is  now  a  tendency 
to  use  a  stroke  of  about  5  inches  in  motors  of  all  sizes.  Pleas- 
ure car  motors  make  about  1800  revolutions  at  normal  speed  or 
at  their  speed  of  maximum  output.  For  pleasure  cars  it  is 
customary  to  use  wheels  of  30  to  36  inches  diameter.  If  we 
assume  that  the  wheels  are  36  inches  in  diameter  and  that  the 
car  is  to  be  geared  to  make  45  miles  per  hour  at  normal  engine 
speed,  then  the  wheels  must  turn  at 

45  X  5,280  X  12 

i=~  —  2  ---  --  =  420  r.  f.  m. 

60  X  36X3.14 

and  the  gear  reduction  ratio  from  the  engine  to  the  road  wheels 
must  be  1800  to  420,  or  about  4.25  to  1.  This  ratio  can  easily 
be  obtained  by  means  of  a  single  reduction  gear  of  the  helical 
bevel  type. 

Now  let  us  take  the  case  of  a  heavy  truck  which  has  wheels 
of,  say,  40  inches  diameter  and  is  to  be  geared  to  make  15 
miles  per  hour  at  1,200  revolutions  per  minute  of  the  motor. 
The  driving  wheels  must  then  turn  at 


o4o      3,14 

Hence  the  gear  reduction  ratio  must  be  1,200  to  140,  or  8.5  to 
i.  This  cannot  be  obtained  in  a  practical  way  by  a  single  bevel 
or  spur  gear  set  or  a  chain  and  sprocket  gear,  for  the  reason 
that  the  outside  diameter  of  the  driven  gear  or  sprocket  on 
the  rear  wheels  or  axle  is  limited,  since  the  car  must  clear  the 
road  by  a  certain  amount.  This  reduction  can  be  obtained  by 
means  of  a  worm  and  worm  wheel,  but  if  either  a  bevel  gear  or 
chain  drive  is  used,  a  double  reduction  is  necessary.  It  is  cus- 
tomary in  such  cases  to  employ  a  first  reduction  by  bevel  gears 
to  a  jackshaft  and  a  second  reduction  by  chain  to  the  rear 
wheels,  although  occasionally  the  two  reductions  are  obtained 


GENERAL  STRUCTURE  OF  CAR.  9 

by  means  of  one  spur  gear  set  and  one  bevel  gear  set,  both  con- 
tained in  a  housing  on  the  rear  axle.  All  pleasure  cars 
employ  a  single  reduction  for  normal  speed  operation,  obtained 
by  either  a  set  of  bevel  gears,  a  chain  and  sprocket  wheels  or 
a  worm  and  worm  wheel.  Commercial  vehicles  of  the  lighter 
type  with  pneumatic  tires  are  geared  the  same,  while  the  heavier 
commercial  vehicles  have  either  a  single  worm  gear  reduction  or 
a  double  reduction  by  bevel  gears  and  chains,  by  bevel  gears 
and  spur  gears,  or  by  bevel  gears  and  internal  gears. 

Dead  and  Live  Axles — The  driving  wheels  may  either,,  be 
mounted  upon  bearings  on  the  rear  axle  and  driven  through 
chains  or  spur  gears,  in  which  case  the  axle  is  called  a  dead  axle, 
or  they  may  be  fixed  upon  the  ends  of  driving  shafts  extending 
through  the  rear  axle  housing,  or  be  placed  in  driving  connec- 
tion with  such  shafts  through  driving  dogs  or  positive  clutches, 
in  which  case  the  axle  is  a  live  axle.  Dead  axles  are  used  on  a 
good  many  heavy  commercial  cars  and  live  axles  on  nearly  all 
pleasure  cars.  When  a  dead  axle  is  used  the  rear  wheels  are 
driven  from  a  countershaft — except  in  the  very  few  cases  where 
two  motors  are  used — and  the  differential  gear  is  mounted  on 
the  countershaft.  With  live  axles  it  is  customary  to  mount  the 
differential  gear  at  or  near  the  middle  of  the  axle,  though  some- 
times it  is  mounted  on  the  propeller  shaft  through  which  the 
power  is  transmitted  to  the  driving  axle.  Live  axles  may  be 
driven  through  a  chain  and  sprockets  or  through  bevel,  worm 
or  spur  gears.  Only  a  single  driving  connection  is  required  in 
the  case  of  a  live  axle,  while  in  the  case  of  a  dead  axle  there 
must  be  provided  an  individual  drive  to  each  of  the  driving 
wheels.  Though  the  chain  drive  is  applicable  to  live  axles,  and 
was  at  one  time  extensively  used  on  low  priced  pleasure  cars,  it  is 
now,  as  a  rule,  used  only  in  connection  with  dead  axles,  in 
the  form  of  the  so-called  side  chains.  Nearly  all  live  axles 
of  pleasure  cars  are  driven  through  a  set  of  bevel  gears. 

Frames— One  of  the   rules  which  have  been   established  in 
automobile  design  is  that  the  vehicle  body  should  be  as  inde 
pendent  as  possible  of  the  mechanical  part,  so  that  it  can  be 
removed  without  disturbing  any  of  the  mechanical  parts, 
motor,  transmission  and  control  members  are,  therefore,  carried 
upon  a  substantially  rectangular  frame  made  of  pressed  steel, 
rolled   steel   or  laminated  wood,  which  is   supported  upon  the 
axles  through  the  so-called  body  springs.    The  motor  sets  upon 
this   frame  in  front;  in  the  conventional  type  of  pleasure  car 
chassis  the  motor  space  is  walled  in  by  the  radiator   in  front 


10  GENERAL  STRUCTURE  OF  CAR. 

and  the  dashboard  at  the  rear,  and  the  motor  is  covered  by  a 
sheet  metal  bonnet.  This  same  arrangement  is  also  used  to 
some  extent  in  heavy  commercial  vehicles,  but  for  this  class 
of  vehicles  there  are  two  alternate  arrangements,  viz.,  having 
the  driver's  seat  on  top  of  the  motor  or  at  the  side  of  the  motor. 
In  fact,  there  may  be  said  to  be  still  one  more  alternative,  since 
the  motor  may  be  under  the  seat  proper  or  under  the  footboard 
of  the  driver's  seat.  These  latter  arrangements  make  that  por- 
tion of  the  length  of  the  frame  which  would  otherwise  be  oc- 
cupied by  the  driver's  seat  available  for  loading  space. 

In  the  conventional  type  of  vehicle  the  space  on  the  frame  back 
of  the  dashboard  is  occupied  by  the  body.  It  is  one  of  the 
rules  of  design  that  no  part  of  the  mechanism  back  of  the  dash- 
board, except  the  control  members,  should  project  above  the 
top  plane  of  the  frame.  Formerly  half  elliptic  springs  were 
used  almost  exclusively  and  were  often  placed  directly  under- 
neath the  frame  side  members,  whose  top  edge  was  then  made 
straight  from  end  to  end.  Now,  however,  three-quarter  elliptic 
and  even  full  elliptic  springs  are  widely  used  at  the  rear  on 
pleasure  cars,  and  in  order  to  preserve  a  comparatively  low 
centre  of  gravity,  the  frame  has  a  drop  directly  in  front  of  the 
point  of  attachment  of  the  rear  springs,  or  the  springs,  even  if 
semi-elliptic,  are  placed  outside  the  frame  and  there  is  a  so- 
called  "kick-up"  in  the  frame  directly  over  the  rear  axle,  so  it 
will  not  strike  the  latter  when  the  springs  are  fully  compressed. 
The  frame  side  members  are  generally  swept  in  at  the  front  end 
in  order  to  allow  of  a  greater  limiting  deflection  of  the  steer- 
ing wheels. 

The  so-called  reach  or  perch  has  been  entirely  done  away 
with.  The  rear  axle  transmits  its  driving  thrust  to  the  frame 
either  through  radius  rods  or  the  rear  springs  and  the  frame 
transmits  driving  thrust  to  the  front  axle  through  the  springs. 

Tread  and  Wheel  Base — The  distance  between  the  centre 
lines  of  ground  contact  of  the  wheels  on  opposite  sides  is 
known  as  the  track  or  tread.  This  distance  is  generally  56  inches 
in  pleasure  cars  and  the  lighter  commercial  vehicles,  and  62 
inches  or  more  in  heavy  trucks.  The  National  Automobile 
Chamber  of  Commerce  has  adopted  a  standard  of  56  inches  for 
the  tread  of  pleasure  cars,  but  there  is  no  standard  for  truck 
treads.  Practically  all  light  horse  vehicles  used  in  the  northern 
part  of  the  country  have  a  track  of  56^  inches,  which  is 
measured  from  and  to  the  outside  of  the  tires  at  the  point  of 
contact  with  the  road,  so  an  automobile  with  the  standard  56  inch 
tread  ^will  run  in  ruts  made  by  the  wheels  of  horse  vehicles. 
In  the  South  a  tread  of  60  inches  is  much  used  on  horse  vehicles, 


GENERAL   STRUCTURE   OF   CAR.  11 

and  since  many  of  the  roads  there  are  deeply  rutted  a  large 
part  of  the  year,  several  automobile  manufacturers  have  been 
furnishing  their  cars  with  a  60  inch  tread  to  customers  in  that 
part  of  the  country,  but  the  practice  has  been  discontinued. 

The  distance  between  the  centre  of  road  contact  of  the  front 
and  rear  wheels,  respectively,  is  known  as  the  wheelbase. 
This,  of  course,  is  the  same  as  the  centre  distance  between  the 
axes  of  the  front  and  rear  wheel  spindles.  The  wheelbase 
differs  widely  in  different  types  and  sizes  of  machines.  A  long 
wheelbase  makes  for  a  more  comfortable  riding  car  and  also 
tends  to  prevent  skidding.  On  the  other  hand,  a  long  car  can- 
not be  handled  so  well  in  crowded  streets,  since  it  cannot  turn 
in  such  a  short  radius.  Besides,  a  long  wheelbase  car  is 
necessarily  comparatively  heavy,  since  the  frame  must  be 
made  of  larger  cross  section  in  order  to  support  the  same 
weight,  as  well  as  be  made  longer.  In  passenger  vehicle 
practice  there  is  a  fair  -degree  of  uniformity  with  respect  to 
wheelbases,  the  latter  ranging  between  the  following  limits  for 
different  types  of  cars. 

Four  cylinder  runabouts  and  roadsters,  30  horse  power  and 
under,  90-105  inches. 

Four  cylinder  runabouts  and  roadsters  over  30  and  not  over 
40  horse  power,  105-115  inches. 

Four  cylinder  taxicabs,  4-5  passengers,  96-100  inches. 

Four  cylinder  touring  cars,  30  horse  power  and  under,  100- 
115  inches. 

Four  cylinder  touring  cars  over  30  and  not  over  40  horse 
power,  110-120  inches. 

Four  cylinder  touring  cars  over  40  horse  power,  120-130 
inches. 

Six  cylinder  cars,  about  10  inches  longer  than  four  cylinder 
ones  of  the  same  class. 


CHAPTER  II. 


FRICTION  CLUTCHES. 

The  friction  clutch,  as  already  pointed  out,  serves  the  purpose 
of  connecting  the  motor,  after  it  has  been  started  running,  with 
the  driving  gear  of  the  car,  in  such  a  way  that  the  car  may  be 
gradually  accelerated  and  the  motor  at  the  same  time  pulled  down 
in  speed,  until  the  speeds  of  the  two  correspond,  thus  pre- 
venting shock  and  jar. 

In  motor  cars  employing  a  single  friction  clutch  which  serves 
to  connect  the  engine  to  the  driving  wheels  through  all  of  the 
different  gear  reductions,  the  clutch  is  normally  held  in  engage- 
ment by  a  spring  or  springs,  and  when  it  is  desired  to  discon- 
nect the  engine  in  order  to  stop  the  car,  or  to  change  the  gear, 
the  clutch  is  first  disengaged  by  compressing  its  spring  by  means 
ot  a  pedal,  then  the  gear  is  disengaged  or  changed,  and  finally 
the  clutch  is  let  in  again.  In  other  cars,  where  a  clutch  serves 
for  a  single  gear  reduction  only,  it  is  normally  disengaged,  and 
is  engaged  by  pressure  exerted  on  a  hand  or  foot  lever,  the 
mechanism  transmitting  the  pressure  to  the  frictional  surface  of 
the  clutch  being  self  locking  in  the  engaged  position. 

There  are  quite  a  number  of  different  types  of  clutches,  all 
more  or  less  extensively  used,  viz.: 

Conical  clutches. 

Multiple  disc  clutches. 

Dry  plate  clutches. 

Band  clutches. 

Coil  clutches. 

Expanding  segment  clutches. 

Multiple  disc  and  dry  plate  clutches  are  identical  as  tar  as 
their  general  principle  is  concerned,  but  they  differ  'n  respect  to 
detail  of  design.  Dry  plate  clutches  are  in  very  extensive  use 
on  American  cars,  as  are  conical  clutches.  The  latter  are  par- 
ticularly suited  to  cars  of  relatively  low  power.  Lubricated 
disc  clutches  also  are  quite  popular,  especially  in  Europe. 
The  other  three  types  mentioned  have  been  used  more  or  less 

12 


FRICTION  CLUTCHES. 


13 


in  the  past,  but  arc  now  seldom  met  with,  the  practice  of 
assembling  cars  from  parts  built  by  specialists  having  tended 
toward  the  standardization  of  types.  The  different  types  of 
clutches  will  be  taken  up  in  succession. 

Cone  Clutch — Conical  clutches  may  again  be  divided  into 
three  sub-classes,  viz.,  the  direct  cone,  the  inverted  cone  and  the 
double  cone  clutch.  The  direct  cone  is  the  oldest  and  most 
popular  of  these  types.  As  shown  in  Fig.  i,  with  this  type  the 
flywheel  is  bored  out  to  form  the  female  cone,  into  which  the 
male  cone  is  forced  by  the  pressure  of  a  coiled  spring  concentric 


FIG.    i. — DIAGRAM    OF    DIRECT    FIG.  2. — DIAGRAM  OF  INVERTED 
CONE  CLUTCH.  CONE  CLUTCH. 

with  its  hub.  In  the  inverted  cone  clutch  (Fig.  2)  the  female  cone 
is  formed  by  a  cast  iron  or  steel  ring  bolted  to  the  rim  of  the 
flywheel,  into  which  the  male  cone  enters  from  the  flywheel  or 
engine  end.  The  inverted  type  of  cone  clutch  was  originally 
adopted  in  order  to  make  it  possible  to  place  the  change  gear  box 
nearer  the  engine,  under  the  floor  boards  of  the  driver's  seat, 
since  the  clutch  spring  is  placed  between  the  flywheel  and  the 
clutch  cone,  instead  of  to  the  rear  of  the  latter.  The  double  cone 
clutch  is  a  combination  of  a  direct  and  an  inverted  cone  clutch, 
and  is  particularly  suited  where  great  powers  have  to  be  trans- 
mitted. 


14  FRICTION   CLUTCHES. 

Clutch  Calculations—  In  calculating  any  part  of  the  trans- 
mission we  will  assume  that  the  mean  effective  pressure  in  the 
engine  cylinder  multiplied  by  the  mechanical  efficiency  (T?  p  )  is  80 
pounds  per  square  inch  at  low  engine  speeds  and  65  pounds  per 
square  inch  at  the  speed  of  maximum  output.  These  figures  are 
fairly  representative  though  a  little  low  for  some  engines.  Now 
let  &  =  bore  of  cylinder  in  inches. 

/=  length  of  stroke  in  inches. 
n  —  number  of  cylinders. 
p  =  mean  effective  pressure. 
P  =  mean  total  pressure  on  one  piston. 
T-  torque  in  pounds-feet. 

Then    the    energy    developed    during    one    revolution   of    the 
crankshaft  is 

n  TT  I 


E  =  ~        £2/^~I  foot-pounds. 

If  there  is  a  torque  T  on  the  engine  shaft,  or  a  turning  effort 
of  T  pounds  at  a  radius  of  I  foot,  the  energy  transmitted  during 
one  revolution  is 

E=2ir  Tfoot  pounds. 
Hence 


and 

nib2  p 
T  -        Ig2     pounds-feet  .....................................  (i) 

A  diagram  of  a  cone  clutch  is  shown  in  Fig.  3.  The  spring 
pressure  P  forces  the  male  cone  against  the  female  cone,  pro- 
ducing a  normal  pressure  N  at  their  contact  surface.  According 
to  the  principle  of  the  parallelogram  of  forces 

P  _ 
^  —  sin  a, 

hence 

P  —  Nsin  a.  ................................................  (2) 

where  a  is  the  angle  of  the  clutch  cone.  The  adherence  or 
frictional  force  F  between  the  clutch  cones  is  equal  to  the 
normal  pressure  multiplied  by  the  coefficient  of  friction  / 

F=Nf 

Angle  of  Cone  —  Cone  clutches  faced  with  leather  or  asbestos 
fabric  are  given  an  angle  of  cone  of  from  10  to  13  degrees, 
but  the  most  common  angles  are  12  and  i2l/2  degrees.  .  With 
metal  to  metal  clutches  an  angle  of  10  degrees  can  be  used 
without  risk  of  trouble,  but  such  a  small  angle  in  a  leather 


FRICTION   CLUTCHES  15 

faced  clutch  is  liable  to  cause  it  to  stick.  From  equation  (2) 
it  will  be  seen  that  the  spring  pressure  P  required  to  produce 
a  certain  normal  pressure  decreases  as  the  angle  of  the  cone 
decreases,  hence  there  is  an  advantage  in  using  as  small  an 
angle  as  practical.  However,  a  cone  with  a  relatively  large 
angle  is  less  given  to  "fierceness"  in  action,  i.  e.,  sudden 
gripping. 

Coefficients  of  Friction — The  coefficient  of  friction  between 
leather  and  cast  iron  varies  greatly  according  to  the  condition 
of  the  cast  iron  surface  and  the  state  of  lubrication.  James 
Angelino  in  experiments  made  with  a  piece  of  old  clutch  leather 
found  the  coefficient  of  friction  to  vary  from  f  =  o.i$  to  f  = 


FIG.  3.— COMPOSITION  OF  CONE  CLUTCH  FORCES. 
Kent  gives  the  coefficient  of  leather  on  greasy  metals  as  0.23 
In  the  calculations  it,  therefore,  is  the  best  plan  to  figure  on  a 
coefficient  of  friction  of  0.2,  since  the  leather  is  generally 
boiled  in  tallow  or  soaked  in  castor  oil  prior  to  being  applied 
to  the  clutch,  and  hence  is  always  somewhat  greasy.  Cast 
iron  on  cast  iron  cone  clutches,  lubricated,  have  been  used  to 
some  extent,  and  in  their  case  the  friction  coefficient  is  com- 
paratively low,  not  exceeding  0.07,  depending  upon  the  nature 
of  the  lubricant.  Asbestos  fabric  is  also  used  to  some  extent 
as  a  facing  for  clutch  cones.  It  possesses  the  advantage  that 
it  is  not  affected  by  high  temperatures.  The  coefficient  of  friction 
is  also  somewhat  greater  than  that  of  leather. 


16  FRICTION    CLUTCHES. 

Diameter  of  Cone — It  is  desirable  to  make  the  diameter 
of  the  cone  small,  for  the  following  reason:  The  sliding  gears 
or  jaw  clutches  of  the  change  gear  practically  never  run  at 
equal  peripheral  speeds  just  previous  to  being  meshed,  but 
from  the  moment  they  become  meshed  they  must  run  at  the 
same  speed.  This  means  that  at  the  moment  of  engagement 
one  of  the  connected  parts  must  suddenly  change  its  speed,  and 
this  results  in  a  clash  or  hammer  blow  at  the  point  of  engage- 
ment. Now,  one  of  these  parts  is  mechanically  or  positively 
connected  to  the  driving  wheels  of  the  car,  and  therefore  can- 
not quickly  change  its  speed.  The  other  consists  of  the  clutch 
cone  and  of  a  train  of  gears,  and  the  resistance  to  a  change  in 
the  speed  of  .these  parts  is  proportional  to  the  sum  of  their 
polar  inertias,  of  which  the  inertia  of  the  clutch  cone  is  by  far 
the  greatest.  The  inertia  of  a  revolving  body  is  proportional 
to  its  weight,  and  to  the  square  of  its  radius  of  gyration,  which 
latter,  in  the  case  of  a  clutch  cone,  varies  substantially  as  the 
mean  outside  diameter.  Hence,  the  force  of  the  clash  increases 
and  decreases  substantially  as  the  square  of  the  mean  outside 
diameter  or  radius  of  the  cone.  On  the  other  hand,  the  radius 
must  be  made  large  enough  to  keep  down  the  unit  normal 
pressure  (which  determines  the  wear  of  the  clutch  facing)  and 
the  spring  pressure  required  to  transmit  the  torque  of  the 
motor,  since  a  clutch  with  a  very  stiff  spring  is  "harsh"  and 
difficult  to  operate.  As  a  general  rule,  the  flywheel  would  be 
designed  first  and  the  clutch  made  of  a  corresponding  diameter. 

Unit  Normal  Pressure — In  conical  clutches  lined  with 
leather,  asbestos  fabric  or  similar  material  the  unit  normal 
pressure  generally  ranges  around  12  pounds  per  square  inch. 
However,  in  some  of  the  largest  cone  clutches  it  is  nearly  20 
pounds  per  square  inch,  and  yet  satisfactory  service  is  ob- 
tained. Cone  clutches  are  used  mainly  for  the  smaller  engines 
and  multiple  disc  clutches  for  larger  powers,  and  if  the  former 
are  used  on  engines  of  60  horse  power  and  over  it  is  necessary 
to  employ  large  unit  pressures,  because  the  available  diameter 
is  not  much  greater  than  is  used  in  clutches  for  smaller  powers, 
and  unduly  wide  clutch  faces  are  also  out  of  the  question. 
While  the  clutches  work  satisfactorily  under  the  higher  pres- 
sures, it  is  natural  to  expect  them  to  wear  out  quicker,  and 
wherever  the  space  available  permits  it  is  best  to  keep  the  unit 
pressure  down  to  12  pounds.  In  metal-to-metal  cone  clutches 
the  unit  normal  pressure  must  be  several  times  that  used  with 
leather  faced  clutches  in  order  to  transmit  the  same  power. 


FRICTION    CLUTCHES 


17 


The  foregoing  figures  are  based  upon  the  normal  pressure  re- 
quired to  hold  the  clutch  from  slipping  when  fully  engaged.  The 
actual  normal  pressures  are  some- 
what greater  because  the  clutch  spring 
must  be  made  stronger  than  required 
to  produce  this  normal  pressure 
under  conditions  of  rest.  Suppose 
that  the  normal  pressure*  N  is  just 
insufficient  to  produce  the  necessary 
driving  torque  and  the  clutch  slips. 
The  normal  pressure  can  only  be  in- 
creased by  forcing  the  cone  further 
into  the  flywheel,  and  this  necessitates 
overcoming  the  resistance  to  .motion 
of  the  leather  over  the  cast  iron  sur- 
face in  a  direction  normal  to  that  of 
slippage. 

Referring  to  Fig.  4,  let  N  repre- 
sent the  effective  normal  pressure 
between  the  clutch  friction  surfaces, 
and  P  the  spring  pressure  necessary 
to  produce  this  normal  pressure. 
Let  F  represent  the  frictional  force 
in  the  direction  of  a  generatrix  of 
the  cone;  Pi,  its  component  parallel 
to  the  clutch  axis,  and  0  the  so-called 
friction  angle  (tan  0  =  /),  then 

P  =  N  sin  a, 

F  =  N  tan  <i> 
and 

Pi  —F  cos  a==  N  tan  <j>  cos  <*. 

The  total  spring  pressure  necessary  to  cause  the  clutch  to  engage 
firmly  without  slipping  is 

P2  =  P  +  Pi  =  N  (sin  a  +  cos  a  tan  0) (3) 

In  applying  this  equation  it  is  permissible  to  use  for  tan  <i>  a  con- 
siderably smaller  value  than  the  normal  coefficient  of  friction 
between  leather  and  cast  iron.  This  is  due  to  the  fact  that  when 
one  body  moves  frictionally  over  another  in  a  given  direction,  it 
requires  but  an  insignificant  effort  to  start  it  moving  at  right 
angles  to  its  original  direction  of  motion.  That  is,  the  coeffi- 
cient of  friction  encountered  in  any  given  direction  is  virtually 
reduced  by  motion  in  a  direction  at  right  angles  thereto.  An 
illustration  of  this  principle  is  furnished  by  the  fact  that  when  a 


FIG.   4. — COMPOSITION   OF 

CLUTCH  FORCES  DURING 

ENGAGEMENT. 


18  FRICTION   CLUTCHES. 

mechanic  wants  to  force  a  tight  fitting  collar  over  a  shaft  he 
will  twist  it  angularly  back  and  forth  on  the  shaft,  whereby  the 
effort  required  to  move  it  in  an  axial  direction  is  greatly  reduced. 
We  may  assume  that  the  coefficient  of  friction  in  this  case  is 
one-fourth   of   its   normal   value,   or   0.05.     Hence,   the   general 
equation  for  the  spring  force  required  to  engage  a  leather-faced 
cone  clutch  becomes 
P  =  N  (sin  a  +  0.05  cos  a)  ............  *.  .....................  (4) 

The  frictional  force  at  the  mean  circumference  of  the  cone  is 

TX  12 

—  pounds. 
^m 

The  area  of  the  cone  face  is 

2  ir  rm  w, 

and  since  there  is  to  be  a  normal  pressure  of  12  pounds  per 
square  inch,  the  total  normal  pressure  is 

12   X    2  7T  rm  TV  =  24  7T  rm  "W. 

This   multiplied   by   the   friction   coefficient   0.2   gives   the   total 
frictional  force  — 

O.2    X   24  7T  rm  IV  =  4.8  7T  rm  tV. 

Equating  this  to  the  expression  for  the  frictional  force  found 
above,  we  have 

TX  12 

—  -  -  =  4.8  TT  rm  iv, 

rm 

and 

•"-srr^n  .............................................  (5) 

from  which  equation  the  necessary  width  of  face  may  be  found. 

It  is  also  possible  to  derive  an  equation  for  the  necessary 
spring  pressure  in  terms  of  the  fundamental  clutch  data.  The 
normal  pressure 

N  =  12  X  2  if  rm  TV  =  24  TT  rm  w. 

Substituting  the  value  of  w,  found  above, 


and  substituting  this  value  of  N  in  equation  (4)  we  have 

xr         *r» 

p  _  -  (sz-n  a  _f.  0  .05  cos  a)  ...............................  (6) 

'  m 

In  order  to  facilitate  the  determination  of  the  necessary  face 
width  and  spring  pressure,  according  to  equations  (5)  and  (6), 
Chart  I  has  been  drawn.  From  this  chart  can  be  found  the 
low  speed  torque  of  four  and  six  cylinder  motors  of  any  cyl- 
inder dimensions  within  the  usual  range  of  automobile  practice, 
as  well  as  the  necessary  width  of  clutch  face  and  of  the  clutch 


FRICTION  CLUTCHES. 


19 


Spring  Pressure   For    Six     Cylinder  JYIofor 

Lbs.    300                   450                   JOO                    750  900                 W50 

f"~            Spring  Pressure    for   Four   Cylinder  Motor 

Lbs.    200 JOO 400 500  600                700 


Face          5      Width      For        4"  Six   Cylinders 


CHART  i.— GIVING  Low  SPEED  TORQUE  OF  FOUR  AND  Six  CYLINDER 

MOTORS    AND    WIDTH    OF   FACE   AND    SPRING    PRESSURE 

REQUIRED  FOR  A  LEATHER-FACED  CONE  CLUTCH 

TO  TRANSMIT  THIS  TORQUE. 


20  FRICTION   CLUTCHES. 

spring  pressure  required  with  different  mean  radii  of  clutch  and 
angles  of  cone.  The  method  of  using  the  chart  is  indicated  in 
diagram. 

Constructional  Details — Since  the  inertia  of  the  clutch  must 
be  as  small  as  possible,  the  clutch  cone  is  generally  cast  of 
aluminum,  though  of  late  pressed  steel  clutches  have  come  into 
quite  extensive  use,  mainly  abroad.  In  the  case  of  aluminum 
cones  the  rim  is  generally  made  of  a  mean  thickness  of 
one-quarter  inch,  tapering  from  the  edges  toward  the  joint 
with  the  web,  which  latter  should  preferably  be  at  the  middle 
of  the  rim.  In  order  to  obtain  the  necessary  strength  in  the  web 
with  the  least  amount  of  material  the  latter,  instead  of  being  made 
radial,  is  inclined  considerably  toward  its  axis,  so  the  material  will 
work  partly  under  compression.  The  dimensions  of  the  web  or 
spokes  are  largely  a  matter  of  foundry  limitations.  For  the  smaller 
powers  a  plain  web  is  used,  tapering  from  about  three-sixteenths 
inch  near  the  rim  to  one-quarter  inch  where  it  joins  to  the  steel 
centre,  which  is  lightened  by  large  holes  being  formed  in  it. 
Some  designers,  however,  prefer  to  leave  the  rim  solid,  as  it 
keeps  out  dust.  When  spokes  are  used  they  are  often  of  cross- 
shaped  section  or  ribbed,  so  as  to  provide  additional  lateral 
strength  in  the  cone  and  also  to  support  the  rim  more  rigidly. 

Clutch  leather  is  generally  treated  before  being  applied  to 
the  clutch  by  being  either  boiled  in  tallow  or  soaked  in  castor 
oil,  the  excess  oil  or  grease  being  removed  by  passing  the  leather 
through  rolls.  The  leather  must  be  cut  to  form  a  sector  of  an 
annular  ring  of  an  inside  radius  o-a  and  an  outside  radius  o-b 
(Fig.  3).  The*  length  of  the  inner  edge  of  the  annular  sector 
must  evidently  be  2  TT  r,  Now,  the  radius 

r 

o-a  =  — : — ' 
stna. 

and  the  circumference  of  a  circle  of  radius  o-a  therefore  is 

2  TT  r 

sin  a 

Hence  the  angle  0  to   which   the  leather  should  be  cut  can  bt 
found  from  the  proportion 

2  irr 

— —  :  360  degrees  =  2  v  r  :  <f> 

<f>  =  sin  a  X  360  degrees. 

Therefore,  in  laying  out  the  pattern  of  the  leather  (Fig.  5), 
strike  two  concentric  circles  of  radii 

and  o.fr  --  — : —  4-  -uj 

stria  ' 


FRICTION  CLUTCHES. 


21 


where  w  is  the  width  of  the  face  of  the  clutch.  Then  from  the 
annular  ring  thus  formed  cut  out  a  sector  subtending  an  angle 
sin  a  X  360  degrees  at  the  centre. 

Some  designers  form  a  small  radial  flange  on  the  edge  of  the 
rim  at  its  bigger  end  which  will  retain  the  facing,  and  thus  take 
some  of  the  stress  off  the  retaining  means  and  off  the  facing 
itself.  When  leather  facing  is  used  it  is  retained  by  means  of 
copper  rivets  whose  heads  are  countersunk  beneath  the  surface 
of  the  leather  and  whose  ends  on  the  inside  of  the  clutch  rim 
are  hammered  over.  Usually  two  rows  of  one-eighth  inch  rivets 
are  used,  spaced  about  an  inch  apart.  After  the  leather  is  riveted 


FIG.  5.— PATTERN  FOR  CLUTCH  LEATHER. 

to  the  cone  it  is  accurately  turned  off  in  a  lathe.  An  improved 
method  of  holding  the  leather  in  place  consists  in  the  use  of 
six  or  eight  T  bolts,  and  the  provision  of  depressions  in  the  rim 
of  the  cone  parallel  with  generatrices  of  the  latter,  for  the  re- 
ception of  the  heads  of  the  T  bolts.  This  method  of  securing 
the  facing,  which  is  particularly  applicable  to  asbestos  fabric, 
(which  does  not  lend  itself  well  to  riveting)  is  illustrated  in  Fig.  6. 
Provisions  for  Smooth  Engagement — Cone  clutches  have  a 
tendency  to  grip  with  a  jerk,  especially  in  case  the  car  is  oper- 


22 


FRICTION  CLUTCHES. 


FIG.  6. — CLUTCH  LEATHER  FASTENED  BY  T-BOLTS. 

ated  by  a  novice  driver  or  the  clutch  operating  linkage  is  such 
that  the  driver  must  exert  a  very  strong  pressure  on  the  clutch 
pedal.  In  order  to  overcome  this  tendency,  which  is  detrimental 
to  the  whole  car,  various  devices  are  resorted  to,  all  based  on 
the  principle  that  a  portion  of  one  of  the  engaging  surfaces  is 
raised  by  spring  force  above  its  normal  height,  and  thus  that 
portion  alone  first  contacts  with  the  opposing  surface.  The  plan 
most  commonly  followed  consists  (Fig.  7)  in  turning  a  shallow 
circumferential  groove  on  the  outside  of  the  aluminum  cone  near 
its  large  end,  in  which  are  placed  a  number  of  equally  spaced 
flat  steel  springs  which  are  fastened  to  the  cone  by  one  rivet 
each,  or  to  a  screw  secured  in  the  rim  of  the  cone.  These  steel 
springs  are  of  such  form  that  they  slightly  lift  the  leather  when 
the  clutch  is  disengaged,  so  that  certain  portions  of  the  leather 
come  in  contact  with  the  flywheel  rim  first.  These  "auxiliary" 
springs  are  fully  extended  when  the  clutch  surfaces  first  engage 
each  other,  and  the  pressure  of  contact  therefore  starts  from 
nothing. 

A  similar  device,  comprising  coiled  instead  of  flat  springs,  is 
illustrated  in  Fig.  8.  It  consists  of  a  small  shell  cast  integral  with 
or.  riveted  to  the  clutch  rim  from  the  inside,  which  contains  a 
coiled  spring  and  a  plunger  pressed  outward  thereby.  The  head 


FIG.  7. — FLAT  SPRING  UNDEP  CLUTCH  FACING. 


FRICTION   CLUTCHES. 


23 


of  the  plunger,  which  presses  against  the  clutch  facing  from 
underneath,  may  be  either  fillister  shaped  or  in  the  form  of  a 
crossbar  extending  underneath  the  leather  the  entire  width  of 
the  clutch  face. 

Where  either  a  male  or  female  cone  of  steel  is  used  it  is  pos- 
sible to  cut  slits  in  it  length- 
wise and  circumferentially,  as 
shown  in  Fig.  9,  or  at  an 
angle  to  the  edge,  and  then 
bend  the  flaps  so  formed 
slightly  outward  or  inward,  as 
the  case  may  be.  This  prac- 
tice is  or  has  been  followed 
by  Renault,  Cadillac,  Pullman 
and  others. 


FIG.  8. — SPRING  PLUNGER  UNDER 
CLUTCH  FACING. 


Cork  inserts  are  used  with" 
leather-faced  cone  cluches  by 
a  number  of  manufacturers,  mainly  with  the  object  of  making 
the  engagement  more  gradual.  The  properties  of  these  corks 
will  be  discussed  in  connection  with  plate  clutches,  in  which 
they  are  more  extensively  used.  Corks  used  in  leather-faced 
cone  clutches  vary  in  diameter  from 
five-eighths  to  one  inch  and  cover  from 
5  to  30  per  cent,  of-  the  surface  of 
the  cone.  When  the  area  presented 
by  the  corks  does  not  exceed  10  per 
cent,  of  the  total  frictional  area, 
they  do  not  materially  affect  the  co- 
efficient of  friction,  but  some  advan- 
tage is  gained  in  this  respect  when 
from  20  to  30  per  cent,  of  the  surface 
is  made  up  by  the  corks.  The  fric- 
tion is  then  somewhat  greater  than 
that  between  leather  and  cast  iron, 
and  consequently  the  spring  pressure  can  be  reduced. 

Multiple  Springs— A  few  makers  use  three  clutch  springs 
placed  at  equal  angular  distances  and  about  midway  between  the 
clutch  shaft  and  the  rim.  One  advantage  of  this  arrangement 
is  that  the  clutch  is  more  easily  adjusted,  owing  to  the  greater 
accessibility  of  the  adjusting  means.  A  typical  design  of  this 
kind  is  shown  in  Fig.  10.  A  three  armed  spider  is  placed  on 
the  tailshaft  just  behind  the  web  of  the  flywheel,  whose  arms 
carry  studs  or  spring  bolts  extending  backward  parallel  with 


FIG.  9. — SLOTTED  CLUTCH 
FEMALE  CONE. 


FRICTION   CLUTCHES. 


the  tail  shaft,  through 
holes  in  the  web  of  the 
clutch  cone.  The  por- 
tions of  the  three  spring 
bolts  extending  through 
the  clutch  cone  are  sur- 
rounded by  coiled  springs, 
whose  rearward  ends 
bear  against  washers 
supported  by  adjusting 
nuts.  The  spring  thrust 
is  taken  up  on  a  ball 
thrust  bearing  carried  on 
the  tail  shaft.  Construc- 
tions similar  to  the  one 
here  shown  are  used  by 
several  English  manu- 
facturers. 

Clutch  Centre  — The 
clutch  may  be  regarded 
as  composed  of  three 
main  parts,  viz.,  the 
cone  with  its  web  or 
spokes,  the  supporting 
bearing,  and  a  spring  housing  or  hollow  shaft  by  which  the 
power  is  transmitted  to  the  change  gear.  Generally  these 
three  parts  are  made  separate,  though  sometimes  the  cone  is 
formed  integral  with  the  bearing.  The  clutch  bearing  is  oper- 
ating only  when  the  clutch  is  disengaged,  and  evidently  carries 
very  little  load.  It  therefore  may  be  of  relatively  small  diameter 
and  free  fitting.  The  bearing  is  practically  always  a  plain  one, 
and  generally  the  non-fluid  oil  in  the  clutch  spring  housing  is 
depended  upon  for  its  lubrication,  it  being  drilled  with  several 
large  oil  holes  and  cut  with  deep  oil  grooves,  but  some  makers  in 
addition  provide  a  pressure  grease  cup  on  the  outside  of  the 
clutch  which  can  be  screwed  down  at  intervals,  the  grease  being 
forced  through  a  drill  hole  directly  to  the  bearing  surface. 

The  clutch  spring  generally  surrounds  the  bearing,  its  forward 
end  resting  against  a  flange  thereon  and  its  rear  end  against  a 
ball  thrust  bearing  on  the  end  of  the  tailshaft  or  on  a  cap  screw 
screwed  into  the  end  of  that  shaft.  This  thrust  bearing  works 
only  when  the  clutch  is  disengaged,  whereas  when  it  is  engaged 
both  ends  of  the  spring  press  against  parts  rotating  in  unison 
and  incapable  of  moving  further  apart.  In  other  words,  the 


FIG.  io.— MULTIPLE  SPRING  CLUTCH. 


FRICTION   CLUTCHES.  25 

spring  pressure  is  then  self-contained.  This  is  contrary  to  con- 
ditions in  the  earlier  cone  clutches,  in  which  the  clutch  spring 
took  purchase  on  a  shoulder  on  the  transmission  shaft,  thus 
creating  end  thrust  in  both  the  transmission  shaft  and  the  crank- 
shaft 

It  is  quite  desirable  to  keep  down  the  length  of  the  tailshaft, 
so  the  change  gear  box  may  be  located  underneath  the  floor 
boards  of  the  driver's  seat,  and  enough  space  should  be  allowed 
between  the  rear  end  of  the  tailshaft  and  the  forward  end  of  the 
transmission  driving  shaft,  so  the  clutch  can  be  removed  from  the 
car  without  removing  either  the  engine  or  the  gear  box.  If  the 
web  of  the  clutch  cone  is  inclined  backward,  for  the  purpose  of 
increasing  its  strength,  the  flange  for  connecting  it  to  the  clutch 
centre  usually  comes  at  a  considerable  distance  from  the  fly- 
wheel flange,  and  it  is  therefore  advantageous  to  make  the  bear- 
ing of  a  form  similar  to  a  cake  mold,  as  shown  in  Fig.  n,  so  its 
forward  end  will  come  within  a  short  distance  of  the  flywheel, 
making  allowance  only  for  the  wear  of  the  clutch  leather. 

In  designing  the  clutch  centre,  attention  must  be  paid  to  the 
exigencies  of  assembling.  The  clutch  spring  housing  covers  the 
spring  and  extends  beyond  the  end  of  the  tail  shaft,  hence  the 
spring  must  be  put  in  place  and  adjusted  before  the  housing  is 
put  in  place.  Some  makers  bolt  the  web  of  the  cone  and  the 
flange  of  the  bearing  together  by,  say,  three  bolts,  and  pass  three 
intermediate  bolts  through  the  web  of  the  cone  and  the  flanges  of 
both  the  bearing  and  the  clutch  housing.  This  admits  of  assem- 
bling the  cone  with  the  bearing,  then  placing  them  on  the  engine 
tail  shaft,  putting  the  clutch  spring  and  its  retaining  nut  in  place, 
and  finally  bolting  the  clutch  spring  housing  to  the  cone  and 
bearing.  Others  place  the  web  of  the  cone  between  the 
flange  of  the  bearing  and  the  flange  of  the  clutch  spring  housing, 
and  pass  all  of  the  retaining  bolts  through  all  three  connected 
parts.  This  makes  it  necessary  to  assemble  these  parts  after  the 
clutch  spring  is  in  place,  which,  of  course,  can  be  done  only  with 
a  spoked  cone.  Still  other  makers  connect  the  clutch  housing 
with  the  clutch  bearing  by  means  of  radial  bolts  or  set  screws. 

Spring  Thrust  Bearing— When  the  clutch  is  disengaged  and 
at  rest  its  spring  bears  with  one  end  against  a  rotating  part 
(tailshaft  spring  rest)  and  with  its  other  against  a  stationary 
part,  and  to  prevent  undue  wear  and  friction  under  these  condi- 
tions the  spring  usually  exerts  its  pressure  through  a  ball  thrust 
bearing  at  the  rear  end.  In  fact,  if  no  ball  thrust  bearing  were 
provided,  the  friction  between  the  spring  and  its  support  would 


FRICTION   CLUTCHES. 


FRICTION   CLUTCHES.  27 

likely  be  great  enough  to  cause  the  clutch  cone  to  keep  on  spin- 
ning. The  ball  thrust  bearing  may  be  passed  over  the  end  of 
the  tailshaft  and  held  in  place  by  means  of  a  castellated  nut,  or 
this  bearing  may  be  supported  by  means  of  a  cap  screw  screwed 
into  the  end  of  the  tail  shaft.  With  either  arrangement  the 
spring  pressure  may  be  adjusted;  with  the  latter  it  can  be  ad- 
justed through  a  considerable  range,  and,  besides,  the  tail  shaft 
will  be  shorter,  so  the  change  gear  can  be  brought  closer  to  the 
engine.  In  any  case  it  is  necessary  to  provide  a  lock  for  the 
adjustment,  and  with  a  cap  screw  carrying  the  ball  thrust 
bearing  this  lock  usually  assumes  the  form  depicted  in.  Fig.  n. 
The  cap  screw  is  drilled  through  its  centre  and  slightly  tapered 
out  and  split  at  its  outwardly  threaded  end,  to  receive  a  small 
screw,  with  a  correspondingly  tapered  head.  By  means  of  this 
inner  screw  and  its  nut  the  split  end  of  the  cap  screw  can  be 
expanded  and  the  screw  thus  securely  locked  in  place. 

Clutch  Springs—  The  springs  which  hold  the  clutch  in  engage- 
ment are  generally  helical  or  coiled  springs  made  of  either  round 
or  square  steel  wire.  Formulae  for  the  safe  load  and  the  deflec- 
tion of  round  steel  wire  coiled  springs  were  given  in  Vol.  I  in 
the  chapter  on  Valves  and  Valve  Gear.  The  corresponding 
formulas  for  square  steel  wire  springs  are 


=  0.471^- 
n  P  D3 


D  =  mean  diameter  of  coil. 

W  =  maximum  safe  load  in  pounds. 

r  =  compression  of  spring. 

d  =  side  of  cross  section  of  wire. 

n  =  number  of  coils  in  spring. 

5"  =  maximum  safe  fibre  stress  of  material. 

£  =  torsional  modulus  of  elasticity. 

P  =  load  in  pounds. 

Occasionally,  in  order  to  save  space  in  a  longitudinal  direction, 
so-called  volute  springs,  made  of  flat  metal,  as  shown  in  Fig.  12, 
are  used. 

Pressed  Steel  Cones  —  Pressed  steel  cones  are  very  attractive 
to  the  designer,  owing  to  their  light  weight  and  their  low  cost 
when  made  in  large  numbers.  Some  trouble  is  said  to  have  been 
encountered  with  these  cones  owing  to  insufficient  rigidity  and 
consequent  shattering,  and  it  has  been  recommended  to  press*  the 
cone  with  radial  ribs  to  overcome  this  difficulty.  One  English 


28  FRICTION   CLUTCHES. 

manufacturer  makes  the  web  of  his  pressed  steel  cone  in  the 
form  of  a  zone  of  a  sphere,  evidently  with  the  same  object. 
Either  J4  inch  or  3/16  inch  stock  is  used.  A  recent  develop- 
ment in  the  line  of  clutches  is  a  pressed  steel  clutch  with  a 
leather  facing  secured  to  the  driving  cone.  This  should  reduce 
the  moment  of  inertia  of  the  driven  cone  in  such  a  degree  as. to 
eliminate  all  obj  ection  to  the  cone  clutch  on  this  score. 

The  several  designs  of  clutches  here  shown  are  particularly 
simple.  A  great  deal  of  ingenuity  has  been  applied  by  designers 
in  working  out  the  details  of  clutch  centres,  and  much  variety  is 
to  be  found  in  the  designs  extant.  With  cone  clutches  of  the 
inverted  type  it  is  not  easy  to  provide  adjusting  means  for  the 
clutch  spring,  and  none  is  generally  provided. 

Shifting  Collar — To  disengage  a  cone  clutch  the  driven  cone 
must  be  withdrawn  from  the  driving  cone  against  the  pressure  of 
the  clutch  spring.  This  necessitates  a  sliding  connection  between 
the  clutch  pedal  shaft,  which  usually  extends  across  the  vehicle 
frame  directly  above  the  clutch  housing,  and  this  housing.  The 
latter  is  usually  provided  with  a  circumferential  groove,  in  which 
is  located  a  sliding  collar.  If  both  flanges  of  the  groove  are 
integral  with  the  housing,  the  shifting  collar,  of  course,  has  to 
be  made  in  halves  in  order  to  get  it  into  tht  groove,  the  halves 
being  bolted  together.  However,  generally  only  one  flange  of 
the  groove  is  integral,  so  the  shifting  collar  can  be  slipped  over 
the  housing  from  one  end. 

When  the  clutch  is  withdrawn  the  entire  pressure  of  the  clutch 
spring  is  taken  up  on  one  face  of  the  shifting  collar,  and  to 
obviate  the  necessity  of  constant  attention  to  the  lubrication  of 
this  collar  a  ball  thrust  bearing  is  generally  placed  in  the  groove 
to  one  side  of  the  shifting  collar,  so  as  to  take  the  thrust  of  the 
spring.  This,  of  course,  necessitates  the  use  of  one  removable 
flange,  in  order  to  get  the  ball  thrust  bearing  into  place. 

A  typical  shifting  collar  design  is  shown  in  Fig.  14.  The 
collar  itself  is  made  of  brass  and  provided  with  two  radial  pins, 
with  which  engage  the  free  ends  of  the  forked  clutch  shifting 
lever.  These  lever  ends  are  formed  with  oblong  holes  for  the 
pins  to  pass  through,  to  make  allowance  for  the  fact  that  they 
move  in  an  arc  of  a  circle,  while  the  shifting  collar  is  constrained 
to  move  in  a  straight  line.  A  grease  cup  is  usually  screwed  into 
either  one  or  both  of  the  shifting  collar  trunnions. 

In  some  cases  the  shifting  collar  is  made  in  the  form  of  a  cir- 
cular disc,  and  the  forked  shifting  lever  is  made  cam-shaped  and 
bears  against  one  face  of  the  disc.  Pressure  has  to  be  transmitted 


FRICTION  CLUTCHES 


29 


FIG.  12.— VOLUTE  CLUTCH  SPRING. 


FIG.  13.— PRESSED  STEEL  CONE  CLUTCH. 


30  FRICTION  CLUTCHES, 

from  the  clutch  pedal  to  the  clutch  housing  in  one  direction  only, 
and  if  the  clutch  shifter  fork  is  held  against  the  shifting  collar 
by  means  of  a  spring  no  groove  for  the  collar  is  necessary. 

Clutch  Brakes — By  lightening  the  cone,  and  especially  by 
reducing  its  diameter,  it  has  been  endeavored  to  reduce  the  shocks 
due  to  clashing  of  the  gears,  but  there  have  also  been  efforts  in 
other  directions  to  insure  the  possibility  of  smooth  meshing.  The 
clashing,  of  course,  is  due  to  unequal  pitch  velocities  of  the  two 


FIG.  14. — CLUTCH  SHIFTING  COLLAR. 

gears  meshed.  If  the  speed  of  one  of  the  gears  can  be  increased 
or  reduced  previous  to  meshing  until  it  corresponds  to  that  of 
the  other,  then  the  gears  can  be  meshed  without  shock  or  jar. 

Suppose  that  a  car  is  ascending  a  hill  and  it  becomes  necessary 
to  change  to  a  lower  gear.  It  is  evident  that  if  the  second  gear, 
say,  is  disengaged,  and  an  attempt  is  made  to  immediately  engage 
the  first  gear,  the  driven  wheel  of  the  latter  will  run  too  fast  or 
the  driving  pinion  too  slow  to  permit  of  easy  meshing:.  The 


FRICTION    CLUTCHES. 


31 


driver  has  no  control  over  the  driven  gears,  except  through  the 
use  of  the  car  brake,  and  it  would  be  inadvisable  to  apply  that 
while  ascending  a  hill.  However,  as  the  car  is  on  an  up-grade,  its 
speed  and  that  of  the  driven  gear  decrease  rapidly  when  the  motor 
is  disconnected,  and  the  gears  can  be  readily  meshed  after  a  short 
interval  of  time.  In  changing  down  on  the  level  the  driver 
speeds  up  the  pinion  of  the  first  gear  by  allowing  the  clutch  to 
partially  engage  momentarily.  If  the  driver  is  skilled  in  han- 
dling the  clutch  and  gears,  he  will  be  able  to  shift  the  gears 
when  the  two  to  be  engaged  are  running  at  about'  the  same 
pitch  line  velocity. 


FIG.  15. — CLUTCH  BRAKE. 

Thus  in  changing  down  the  gears  automatically  approach  the 
condition  of  equal  pitch  line  velocity,  or  the  condition  of  easy 
mesh.  Not  so  in  changing  up.  The  driven  gear  of  the  pair  to  be 
meshed  is  now  running  too  slowly  and  the  driving  gear  too  fast. 
The  latter  can  only  be  reduced  to  the  proper  speed  by  applying  a 
brake  to  the  clutch.  Many  of  the  larger  cars  are  now  equipped 
with  such  clutch  brakes,  which  act  automatically  when  the  driver 
completely  pulls  out  the  clutch.  One  design  of  such  a  brake  is 
shown  in  Fig.  15.  The  clutch  housing  is  formed  with  a  flange  B, 
against  which  bears  a  fibre  block  A,  carried  on  an  arm  on  the 
clutch  pedal  shaft,  when  the  clutch  pedal  is  fully  depressed. 
Another  type  of  clutch  brake  is  illustrated  in  Fig.  16.  This  is  a 


32 


FRICTION  CLUTCHES. 


clutch  of  the  plate  type,  and  the  power  is  transmitted  from  the 
clutch  shaft  through  a  pinion  and  an  internal  gear,  which  latter  is 
formed  integral  with  a  shaft  coupling  made  in  halves.  This 
coupling  is  provided  with  an  annular  friction  ring  B,  which  when 
the  clutch  is  fully  withdrawn  presses  against  a  corresponding  disc 
A,  secured  to  the  clutch  shifting  ring,  which  latter,  of  course,  does 
not  rotate. 

There  is  quite  a  variety  of  designs  of  clutch  brakes,  the  under- 
lying principle  of  all  of  them  being  that  a  part  rotating  with  the 
clutch  is  brought  into  contact  with  a  non-rotary  part  when  the 
clutch  pedal  is  fully  depressed,  and  the  friction  engendered 
between  the  two  parts  causes  the  speed  of  the  clutch  to  be 
reduced. 


1 

FIG.   16. — Disc  CLUTCH   BRAKE. 

Multiple  Disc  Clutches— Disc  and  plate  clutches  are  based 
on  the  same  principle,  but  constitute  in  a  sense  opposite  extremes 
in  design.  A  disc  clutch  consists  of  two  sets  of  annular  .discs, 
one  set  of  driving  discs  and  one  set  of  driven  discs.  These  are 
placed  together  in  alternate  order,  each  driving  disc  being  located 
between  two  driven  discs.  As  generally  used  on  automobiles,  the 
driving  discs  are  provided  with  key  slots  on  their  outer  circum- 
ference into  which  fit  keys  on  the  inside  of  a  drum  shaped  hous- 
ing secured  to  the  flywheel,  and  the  driven  discs  are  provided 
with  lugs  or  key  slots  on  their  inner  circumference,  which  place 
them  in  driving  connection  with  a  drum  secured  upon  the  driven 
shaft.  Generally  there  is  one  more  driving  disc  than  there  are 


FRICTION   CLUTCHES. 


33 


driven  discs,  so  that  the  two  end  discs  are  of  the  same  kind.  The 
drum  carrying  the  driven  discs  has  a  radial  flange  at  one  end 
which  forms  a  stop  for  the  discs  in  respect  to  axial  motion,  and 
against  the  disc  at  the  other  end  presses  a  compressing  spider  or 
presser,  against  which  the  clutch  spring  exerts  its  pressure. 

Types  of  Disc  Clutches — Multiple  disc  clutches  operating  in 
oil  are  of  three  different  types  of  design,  the  differences  depend- 
ing upon  the  manner  in  which  the  pressure  of  the  clutch  spring  is 
transmitted  to  the  flange  or  back  stop  of  the  discs  on  the  clutch 
drum.  Some  of  these  clutches  employ  three  clutch  springs,  the 


FIG.  17.— MULTIPLE  SPRING  TYPE  OF  Disc  CLUTCH. 

same  as  some  cone  clutches,  and  a  design  of  this  type  is  shown 
in  the  sketch  Fig.  17.  An  outer  drum  A  is  secured  to  the  flywheel 
and  is  provided  with  a  number  of  equally  spaced  keys  on  its 
inner  circumference.  With  these  keys  engage  the  driving  discs, 
which  are  shown  sectioned.  Between  adjacent  driving  discs  are 
located  the  driven  discs,  shown  in  black.  The  latter  are  carried 
on  the  inner  drum  B,  which  is  provided  with  keyways  for  the 
lugs  formed  on  the  inner  circumference  of  the  driven  discs. 
From  the  web  of  the  clutch  drum  B  extend  three  lateral  spring 
bolts  which  carry  the  clutch  springs  C  pressing  against  the  disc 
compressing  spider  D.  Drum  B  is  keyed  to  clutch  shaft  E,  which 
is  connected  with  the  driving  shaft  of  the  change  gear,  and  the 


34 


FRICTION   CLUTCHES. 


disc  compressing  spider  D  is  provided  with  a  hub  surround- 
ing shaft  E  and  a  groove  for  the  clutch  releasing  collar,  or  merely 
a  flange. 

A  multiple  disc  clutch  with  a  single  clutch  spring  surrounding 
the  clutch  shaft  is  illustrated  in  Fig.  18.  The  arrangement  of 
the  outer  drum,  driving  and  driven  discs  and  inner  drum  is  the 
same  as  in  Fig.  17.  In  this  case  one  end  of  the  clutch  spring 
bears  against  an  inward  flange  on  the  hub  of  the  disc  compres- 
sing spider  D,  and  the  other  against  a  collar  on  the  clutch  shaft 
E.  The  latter  has  the  inner  drum  B  securely  keyed  to  it  and 
held  against  endwise  motion  by  a  nut.  Hence,  the  pressure  of 


FIG.  18. — SPRING  PRESSURE  TRANSMITTED  THROUGH  SHAFT. 

the  clutch  spring  is  transmitted  to  the  forward  end  plate  or  stop 
P  of  the  discs  through  the  clutch  shaft  E  and  the  clutch  drum  B. 

In  Fig.  19  is  shown  a  design  of  multiple  disc  clutch  in  which 
the  spring  pressure  is  transmitted  to  the  stop  P  of  the  discs 
through  the  clutch  housing  A.  The  most  forward  disc  bears 
against  a  stop  ring  P  secured  to  the  flywheel  and  against  the  rear- 
most disc  presses  the  compression  plate  D  in  the  usual  way.  This 
disc  or  spider  D  is  acted  upon  by  the  coil  spring  C  which  rests 
against  the  flange  of  the  casing  A.  Figs.  17,  18  and  19  are 
sketches  only,  not  showing  all  of  the  necessary  details  of  these 
clutches. 

The  spring  forces  the  separate  ftiscs  together  and  causes  the 


FRICTION   CLUTCHES. 


35 


driven  discs  to  rotate  in  unison  with  the  driving  discs,  provided 
the  resistance  to  the  motion  of  the  driven  discs  is  not  greater  than 
the  adherence  between  the  driving  and  driven  discs.  It  will  read- 
ily be  seen  that  the  pressure  betwen  any  two  discs  is  equal  to 
the  pressure  of  the  spring,  and  the  adherence  or  resistance  to 
slipping  at  any  contact  surface  is  equal  to  the  product  of  the 
spring  pressure  by  the  coefficient  of  friction.  But  if  there  is  slip- 
page on  one  contact  surface  there  must  be  slippage  on  all  of  them, 
and  since  the  pressure  on  any  contact  surface  is  the  same  as  on 
any  other,  the  total  resistance  to  slippage  is  equal  to  the  prod- 
uct of  the  resistance  to  slippage  at  one  surface  by  the  num- 
ber of  contact  surfaces,  which  latter  is  equal  to  one  less  than 


FIG.  19. — SPRING  PRESSURE  TRANSMITTED  THROUGH  CASE. 

the  number  of  discs.  In  a  multiple  disc  clutch  the  frictional  sur- 
face can  be  made  much  greater  than  in  a  cone  clutch,  and  the 
frictional  force  per  unit  surface  can  be  made  smaller. 

Calculation  of  Disc  Clutches — In  Fig.  20  is  shown  one 
disc  of  a  multiple  disc  or  plate  clutch.  In  this  figure  dr  is  the 
width  of  an  extremely  narrow  annular  ring  of  radius  r.  Sup- 
pose that  the  unit  pressure  on  the  surface  of  this  disc  is  p  pounds 
per  square  inch.  The  area  of  the  annular  ring  of  width  dr  is 

A  =  2  if  r  dr 
and  the  normal  pressure  on  it  is 


36 


FRICTION    CLUTCHES. 


N  =  2  T  r  dr  p. 
This  causes  a  frictional  force 

2  TT  r  dr  p  f, 
where  /  is  the  coefficient  of  friction,  and  a  torque 

r        TT  r2  dr  p  f 


12  6 

Now,  in  order  to  find  the  torque  which  the  friction  over  the  entire 
surface  of  the  disc  will  produce  we  have  to  integrate  the  above 
expression  between  the  limits  r0  (outside  radius)  and  n  (inside 
radius) 


Sdrpf 


FIG.  20. 

•* 

=  —  p  f  (n3  —  n*)  pounds-feet, 
18 


(9) 


n  6 

Equation  (9)  is  useful  in  the  case  of  clutches  whose  discs  have 
a  very  small  inside  radius.  In  the  original  type  of  this  clutch  the 
discs  were  often  mounted  directly  upon  the  driven  shaft,  and  the 
inside  radius  of  the  clutch  disc  was  less  than  one-quarter  the 
outside  radius.  However,  in  modern  automobile  clutches  the 
inside  radius  is  generally  more  than  three-fourths  the  outside 
radius,  and  the  so-called  discs  are  really  in  the  form  of  narrow 
annular  rings.  There  are  two  main  reasons  for  making  the  ele- 


FRICTION   CLUTCHES.  37 

ments  of  the  clutch  ring-shaped  rather  than  disc-shaped.  The 
first  is  that  the  wear  of  the  disc  increases  with  the  distance  from 
the  centre  of  rotation,  owing  to  the  fact  that  the  speed  of  slippage 
increases  with  the  distance  from  the  axis.  Hence,  if  there  is  a 
great  proportional  difference  between  the  outside  and  inside  radii, 
the  rates  of  wear  near  the  inner  and  outer  edges  will  be  greatly 
different.  The  result  will  be  that  as  the  outer  portion  of  the  disc 
becomes  thinner  than  the  inner  portion,  the  pressure  over  its  sur- 
face will  become  unevenly  distributed,  the  unit  pressure  being 
greater  near  the  inner  edge  than  near  the  outer  edge,  and  conse- 
quently the  clutch  will  transmit  less  power  than  originally  with 
the  same  spring  pressure. 

The  other  reason  is  that  the  resistance  to  lateral  motion  of 
the  discs  depends  directly  upon  the  pressure  between  the  driven 
discs  and  their  keys  or  keyway  walls,  which  is  less  the  greater 
the  inner  radius  of  the  discs.  When  the  clutch  is  disengaged  the 
discs  are  not  positively  pulled  apart,  but  are  supposed  to  be  either 
jarred  apart  by  the  vibration  or  to  be  forced  apart  by  auxiliary 
springs,  and  especially  in  the  former  case  is  it  desirable  that  the 
resistance  to  their  lateral  motion  be  as  little  as  possible,  as  there 
is  then  less  danger  of  dragging. 

In  the  case  of  clutch  discs  or  rings  whose  inner  radius  is  more 
than  two-thirds  of  the  outer  radius  it  is  permissible  to  consider 
the  engaging  pressure  (and  hence  the  frictional  force)  concen- 
trated at  a  distance  from  the  axis  of  rotation  equal  to  the  arith- 
metical mean  between  the  outer  and  inner  radii  (rm  )  .  The  fric- 
tional force  at  any  contact  surface  then  is  P  f,  the  aggregate  fric- 
tion force  (n  —  i)  P  f,  and  the  moment  of  the  frictional  force  or 
torque. 


In  any  given  problem  of  design  the  torque  to  be  transmitted 
is  a  fixed  quantity,  but  the  limiting  torque  of  the  clutch  is  the 
product  of  four  variables,  viz.,  the  mean  radius  of  the  discs,  the 
number  of  contact  surfaces,  the  spring  pressure  and  the  friction 
coefficient.  Since  these  factors  are  independently  variable,  it  is 
not  surprising  that  practice  in  disc  clutch  design  is  not  in  the 
least  uniform.  The  tendency  is  rather  toward  small  mean  radii 
and  a  very  considerable  number  of  discs,  since  the  inertia 
increases  as  the  square  of  the  radius  and  directly  as  the  number 
of  discs,  whereas  the  capacity  of  the  clutch  increases  directly  with 
both  the  radius  and  the  number  of  discs.  The  coefficient  of  fric- 


38  FRICTION   CLUTCHES. 

tion,  of  course,  can  be  changed  only  by  changing  the  material  of 
the  discs  or  the  lubricant. 

Material  of  Discs — In  the  type  of  disc  clutch  which  has 
been  used  the  longest  in  automobile  practice,  both  sets  of  discs 
are  metallic  and  run  in  oil.  The  discs  are  generally  made  from 
saw  steel,  about  3s  inch  thick,  stamped  rings  of  any  desired 
diameter,  with  driving  lugs  or  key  slots,  as  desired,  being  fur- 
nished by  several  saw  steel  manufacturers.  Some  manufacturers 
believe  that  steel  on  bronze  gives  better  wear  and  make  one  set 
of  the  discs  of  the  latter  material.  Saw  steel  is  a.  very  -suitable 
material,  being  hardened  and  more  uniform  in  thickness  than 
ordinary  sheet  steel.  Sheet  copper  is  also  used  together  with 
sheet  steel.  Whatever  material  is  used,  the  greatest  care  must 
be  exercised  to  get  the  thickness  as  nearly  uniform  as  possible 
and  to  give  the  surfaces  a  smooth  finish. 

Laws  of  Friction — The  coefficient  of  friction  between  metals 
with  lubrication  varies  widely  according  to  conditions.  Some  of 
the  laws  of  friction  which  have  a  bearing  on  the  value  of  the 
coefficient  of  friction  in  disc  clutches  may  be  stated  as  follows: 
The  coefficient  of  friction  between  two  metallic  surfaces  separated 
by  a  film  of  lubricant  is  much  greater  when  the  surfaces  are  at 
rest  relative  to  each  other  than  when  there  is  sliding  motion 
between  them.  The  friction  does  not  depend  so  much  upon  the 
material  of  the  discs  as  upon  the  lubricant.  When  the  discs  are 
stationary  the  coefficient  of  friction  increases  with  the  specific 
pressure.  On  the  contrary,  when  there  is  sliding  motion  between 
the  surfaces  the  coefficient  of  friction  decreases  as  the  specific 
pressure  increases  (up  to  a  certain  limit  which,  however,  is  far 
beyond  the  pressure  used  in  disc  clutches).  The  coefficient  of 
friction  also  varies  with  the  speed;  it  seems  to  be  a  minimum  at 
loo  to  150  feet  per  minute,  increasing  as  the  speed  is  increased  or 
diminished,  and  approaching  the  static  friction  coefficient  at  very 
low  speeds. 

From  the  above  it  will  be  seen  that  it  is  difficult  to  assign  a 
definite  value  to  the  coefficient  of  friction  f  for  use  in  the  calcu- 
lation of  friction  clutches.  However,  the  author  believes  it  to  be 
on  the  safe  side  to  use  a  coefficient  ^  =  0.04  for  steel  on  steel, 
phosphor  bronze  or  copper  with  lubrication. 

Disc  Clutch  Data— Denoting  the  mean  radius  of  the  discs 
by  rm  and  the  number  of  f rictional  surfaces  by  na ,  the  equation 
for  the  limiting  torque  of  a  disc  clutch  may  be  written 


FRICTION   CLUTCHES.  39 


Now,  even  if  the  material  of  the  discs  is  settled,  so  that  /  is  a 
fixed  quantity,  there  remain  three  independent  variables,  and 
the  desired  torque,  therefore,  can  be  obtained  in  many  different 
ways.  In  this  connection  it  is  to  be  remembered  that  if  we 
increase  the  mean  radius  rm  we  increase  the  inertia  of  the 
clutch,  even  if  we  correspondingly  decrease  the  number  of  discs 
so  as  to  retain  the  same  limiting  torque.  On  the  other  hand,  if 
we  increase  either  the  number  of  discs  or  the  spring  pressure  we 
increase  the  work  which  must  be  done  by  the  operator  in  disen- 
gaging the  clutch,  because  the  spring  must  be  compressed  an 
amount  proportional  to  the  number  of  discs,  in  order  that  there 
may  be  sufficient  clearance  between  adjacent  discs,  and  the  work 
done  in  compressing  the  spring  is  measured  by  the  product  of  the 
clutch  spring  pressure  by  the  distance  of  the  compres- 
sion of  the  spring  during  the  process  of  declutching.  The 
foot  has  only  a  small  range  of  comfortable  motion,  and  the 
pressure  which  can  be  exerted  by  it  is  also  limited.  It  is  evident 
that  the  product  Pna  is  a  measure  of  the  work  to  be  done  in  dis- 
engaging a  clutch,  and  it  has  been  found  that  this  product  should 
not  exceed  12,000  if  clutch  operation  is  not  to  be  irksome.  The 
friction  force  per  unit  of  contact  surface  varies  from  0.6  pound 
per  square  inch  to  2  pounds,  the  average  value  being  i  pound. 
In  clutches  of  this  type  (metal-to-metal-in-oil)  the  average  ratio 
of  the  inside  to  the  outside  radius  is  five-sixths. 

If  we  made  Pn,  =  12,000  for  all  clutches,  then  the  small  clutch 
would  be  as  hard  to  operate  as  a  large  one,  which  is  not  exactly 
desirable.  Besides,  the  mean  radius  rm  would  increase  in  direct 
proportion  to  the  torque  to  be  transmitted;  it  should  increase 
with  the  torque,  but  not  in  direct  proportion.  It  may  well  increase 
as  the  square  root  of  the  torque,  and  the  following  equation  gives 
a  good  value: 


3-4 

We    may    therefore    recapitulate    the    rules    for    multiple    disc 
clutch  design  as  follows  : 
n 

-  =s  in  average  practice. 
fo 

Friction  force  =  I  pound  per  square  inch. 
Coefficient  of  friction  /  =  o.O4. 
The  area  of  one  friction  surface  is 

TT  (r02  —  n2)  square  inches. 
and    the    frictional    force   between    adjacent    discs,    expressed    in 


40  FRICTION   CLUTCHES. 

pounds,   is  the  same.     The  total    frictional   force   at   the   mean 
radius  of  the  discs  is 

TX  i2? 

hence  the  number  of  friction  surfaces  required  is 
12  T 
rm  12  T 


ir(r02  —  n2)  —  TT  rm  (r02  — 
and  the  number  of  discs  required 


The  spring  force  required  is 


P=  -v    up  ^      -i (I2) 

Both  of  the  above  equations  can  be  materially  simplified  if  the 
ratio  of  the  inner  to  the  outer  radius  is  fixed. 

For  n=  P  = 

n   _  21.2  T 

^  ~™ 

n  —  A 
,o-f 

r\ 


•£=» 

If  we  assume  an  inner  radius  equal  to  five-sixths  the  outer 
radius  and  substitute  in  the  equations  the  value  of  the  torque 
of  a  -four  cylinder,  4x5  inch  motor  we  find  that  the  mean  radius 
of  the  discs  should  be  3.4  inches,  the  outer  radius  3.71  inches — 
say  3.75  inches — and  the  inner  radius  3.12  inches — say  3^  inches. 
The  number  of  discs  figures  out  to  35  and  the  spring  pressure  to 
337  pounds.  An  uneven  number  of  discs  is  generally  employed. 

When  the  spring  exerts  its  pressure  through  the  clutch  shaft 
or  through  spring  bolts  secured  into  the  web  or  spokes  of  the 
inner  drum,  it  is  well  to  have  one  more  driven  disc,  whereas  when 
the  spring  exerts  its  pressure  through  the  clutch  housing  it  is  best 
to  have  one  more  driving  disc.  In  either  of  these  cases  if  the 


FRICTION   CLUTCHES. 


j^  4"  4±"  5"  ~3p 

Outside      Radius      o/     Discs 
Jf umber    of  Discs 


X 


6" 


41 
/ooo' 

900 


800-% 

s; 


600  ^ 


500  ^ 

> 


400 


300 


\ 

\ 

x 

i 

\ 

N 

\ 

\ 

y 

'  \ 

\ 

\ 

V 

a 

/ 

> 

^ 

s 

\ 

\ 

\ 

f( 

2 

/ 

\ 

/ 

jv 

/ 

/  ^ 

i 

X 

a 

\ 

\ 

E" 

70, 

\ 

xf 

\ 

\ 

i 

,x 

\ 

\ 

\ 

/ 

n\ 

/ 

\ 

/ 

\ 

L 

i 

\ 

\ 

\ 

/ 

x 

^ 

\ 

\ 

/ 

V 

5 

X 

3 

\? 

i" 

X 

\. 

\ 

\ 

>^ 

T" 

2 

7 

"> 

/ 

5 

V 

^ 

\ 

J 

/ 

\ 

\ 

\ 

/ 

? 

V  «- 

V 

\ 

/ 

/ 

\ 

\ 

\ 

^ 

A 

\ 

\ 

\ 

\ 

/ 

\ 

/ 

\ 

^ 

\J 

^ 

\ 

\ 

x 

X 

\ 

\ 

3 

\ 

x 

\ 

X 

^ 

>( 

/ 

/ 

\ 

/ 

\ 

SX 

/N 

\ 

fr 

X" 

\ 

\ 

\ 

s 

\\ 

x 

X 

\ 

/ 

/ 

s 

/ 

/ 

\ 

x 

*> 

> 

r 

\ 

\ 

X 

X 
\ 

\N 

\ 

\ 

r0  = 

X 

*s^ 

/^ 

V 

x 

\ 

\  / 

7 

\ 

x 

A 

\ 

^ 

2 

\ 

A 

\ 

\^ 

\ 

X, 

/ 

/ 

x 

x 

'  \ 

\^ 

x 

\ 

> 

X 

\ 

\ 
j 

\ 

X 

x\ 

\ 

\\ 

\ 

X 

/ 

/ 

y 

N 

/ 

/ 

^ 

\ 

x 

X  \ 

\ 

x 

XI 

\ 

^ 

f\ 

\ 

\ 

\ 

\\ 

^x 

/ 

/ 

/ 

/ 

? 

> 

^ 

/ 

x 

s 

s  X 

x 

\ 

V 

X 

\ 

\ 

\ 

\ 

v 

V 

Ss. 

V 

/ 

/ 

x 

\, 

,x 

/ 

N 

s^ 

x 

\ 

\ 

x 

^ 

\ 

\ 

\ 

\ 

^  \ 

\ 

J 

/ 

/ 

< 

7 

/ 

/ 

X 

< 

"x^x* 

x 

\ 

>x 

x 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

V 

\\ 

/ 

/ 

/ 

x 

/ 

K 

x 

x 

X 

s 

^\, 

X 

\ 

\ 

\ 

\ 

\ 

\ 

\, 

\v 

\\ 

/ 

/ 

/ 

x 

x 

< 

\ 

Sj 

x 

X 

\ 

\ 

\ 

** 

\ 

\ 
\ 

A 

/ 

X 

/ 

x 

x 

x 

X 

" 

\ 

^ 

\ 

\ 

x 

X 

\ 

\ 

\ 

\ 

\ 

\ 

\ 
\ 

A 

7"orque     in    J^ou nets- feet 

CHART  II.— GIVING  NUMBER  OF  Discs  AND  SPRING  PRESSURE  RE- 
QUIRED   IN     MULTIPLE-DlSC-IN-OlL    CLUTCHES. 


42 


FRICTION   CLUTCHES. 


clutch  is  slipping  there  will  be  no  relative  rotary  motion  between 
the  two  parts  against  which  the  clutch  spring  bears,  hence  no  ball 
thrust  bearing  will  be  required  to  take  up  the  thrust  of  the  spring. 

Number  of  discs  and  spring  pressures  required  in  metal-to- 
metal  multiple  disc  clutches  can  be  readily  found  from  Chart  II, 
after  the  torque  of  the  motor  has  been  obtained  from  Chart  I. 
Chart  II  is  based  on  a  unit  frictional  force  of  i  pound  per  square 
inch  and  a  coefficient  of  friction  of  0.04.  If  a  very  light  clutch 
is  desired  the  number  of  discs  found  from  the  chart  can  be  re- 
duced, and  the  spring  pressure  found  increased  in  proportion. 

Methods  of  Releasing  Discs— In  order  to  insure  positive 
separation  of  the  discs  when  the  spring  pressure  is  removed,  and 
thus  prevent  dragging  of  the  clutch,  it  is  necessary  to  provide 


FIG.  21. — METHODS  OF  SEPARATING  Discs. 

alternate  discs  with  tongues  sprung  to  one  side,  as  shown  in  Fig. 
21  at  A,  or  some  similar  means.  Two  such  tongues  on  each 
driving  disc,  one  opposite  the  other,  are  sufficient.  An  alternate 
method  of  insuring  positive  separation  is  illustrated  in  the  same 
figure  at  B,  and  consists  in  providing  the  driving  discs  with 
radial  lugs  on  the  outside  circumference  into  which  are  riveted 
buttons  whose  heads  are  slightly  thicker  than  the  driven  discs,  so 
that  the  lugs  are  slightly  sprung  when  the  discs  are  forced  to- 
gether by  the  clutch  spring.  The  driving  discs  may  be  provided 
with  four  lugs,  at  quarters,  and  rivets  inserted  into  two  of  these 
lugs,  located  oppositely.  The  discs  may  then  be  assembled  in 
such  a  manner  that  the  riveted  lugs  of  adjacent  driving  discs  are 
at  quarters.  Where  separating  springs  of  this  kind  are  used, 
the  clutch  spring  must  be  made  sufficiently  strong  to  overcome 


FRICTION   CLUTCHES. 


43 


the  force  of  these  springs  and  still  give  enough  frictional  force 
between  the  discs. 

Constructional  Details—Multiple  disc  clutches,  the  same  as 
other  types,  are  generally  combined  with  the  flywheel,  but  occa- 
sionally they  are  enclosed  in  a  special  compartment  of  the  change 
gear  case,  which  can  be  done  without  difficulty,  since  these 
clutches  can  be  made  of  a  relatively  small  diameter.  When  thus 
enclosed  in  the  gear  box  or  when  used  in  a  unit  power  plant, 
there  is  no  need  to  specially  enclose  the  clutch.  But  in  other 
cases  an  oil-tight  housing  must  be  provided.  This  housing  is 
sometimes  made  of  one-eighth  inch  pressed  steel  in  a  single 
piece,  with  a  radial  flange  at  its  open  end  for  bolting  to  the 
flywheel  web  and  a  hub  portion  either  formed  integral  or  riveted 


FIG.  22. — METHODS  OF  DRIVING  Discs. 

to  it  which  takes  the  adjusting  bushing  for  the  spring  if  the 
spring  pressure  is  transmitted  through  the  housing,  and  forms 
an  oil-tight  joint  with  the  hub  of  the  disc  compressing  spider. 
This  housing  may  also  be  made  of  two  castings — a  cylindrical 
shell  and  an  end  plate.  Some  designers  even  provide  a  stuffing 
box  in  the  hub  of  the  clutch  housing  to  insure  oil  tightness. 

If  the  clutch  has  no  special  housing  it  may  be  driven  from  the 
flywheel  by  radially  extending  driving  pins  secured  into  the  web 
of  the  latter  (A,  Fig.  22).  If  a  housing  is  used  the  driving  is 
done  either  through  keys  riveted  to  the  cylindrical  shell  (B,  Fig. 
22),  or  through  bolts  which  hold  both  the  shell  and  the  end  plate 
to  the  flywheel  (C,  Fig.  22).  The  key  slots  on  the  outside  of  the 


44 


FRICTION   CLUTCHES. 


driving  discs  are  cut  either  in  the  full  ring,  or  the  rings  are 
formed  with  driving  lugs  which  have  key  slots  or  driving  pin 
holes  cut  in  them.  The  latter  form  of  construction  leads  to  a 
saving  in  weight,  but  necessitates  a  somewhat  more  expensive 
die  for  stamping  out  the  discs.  In  any  case,  there  must  be  a 
liberal  clearance  between  the  inner  surface  of  the  driving  keys 
and  the  outer  edge  of  the  driven  discs  and  between  the  inner 
edge  of  the  driving  discs  and  the  surface  of  the  inner  drum  so 
there  will  be  no  dragging  owing  to  contact  at  these  surfaces  after 
slight  wear. 

Practice  as  to  the  number  of  driving  pins  or  keys  and  driving 
lugs  on  the  driven  discs  varies  greatly.  Some  designers  pro- 
vide as  many  as  ten  or  twelve 
large  size  keys,  which  seems 
to  be  more  than  necessary. 
The  number  and  size  of 
keys  do  nol  affect  the 
freedom  of  lateral  motion 
of  the  discs,  but,  of  course 
affect  the  wear  of  keys  and 
key  slots,  but  clutches  with 
only  three  one-half  inch 
driving  pins  with  an  aggre- 
gate maximum  pressure  of 
three  hundred  pounds  on 
them  are  known  to  give 
good  results. 

It  is  generally  considered 
that  one-hundredth  of  an 
inch  is  the  minimum  clear- 
ance between  discs  which 
will  insure  freedom  from 
dragging,  and  in  the  de- 
sign of  the  housing  and 
the  inner  drum  allowance 
must  be  made  for  end 

motion  of  at  least    —  inch.     In  practice   the   allowance  made 

TOO 

varies  from  i/ioo  to  1/64  inch  per  friction  surface.  However, 
one  well  known  manufacturer  of  multiple  disc  clutches  allow? 
only  from  1/125  to  1/175  inch. 

The  inner  drum  or  the  shaft  to  which  it  is  secured  is  usually 
supported  upon  or  in  a  radial  ball  bearing.    The  reason  for  the 


FIG.  23. — INNER  DRUM. 


FRICTION   CLUTCHES. 


45 


use  of  a  ball  bearing  at  this  point  is  that  the  bearing,  if  plain, 
would  be  hard  to  lubricate  effectively  except  through  the  engine 
tailshaft,  and,  besides,  the  friction  of  this  bearing  tends  to  pro- 
duce dragging,  and  the  tendency  to  drag  is  already  the  weak 
point  of  the  multiple  disc  clutch.  Usually  the  radial  bearing  is 
carried  upon  a  short  tailshaft,  and  its  outer  race  is  forced  into  a 
counterbore  in  the  drum,  but  in  some  constructions  the  bearing 
is  carried  upon  the  end  of  the  clutch  shaft  and  its  outer  race 
rests  in  the  bore  of  the  flywheel  web.  The  drum  (Fig.  23)  is 
preferably  made  of  a  steel  or  malleable  iron  casting  and  milled 
with  from  four  to  twelve  key  slots  in  which  engage  the  key  lugs 
formed  on  the  driven  discs.  The  end  plate  which  forms  the  stop 
for  the  discs  is  made  separate  from  the  drum  and  is  secured  to 
its  rim  by  machine  screws,  or  else  passed  over  the  drum  against 
a  small  flange  turned  thereon. 

The  rim  of  the  drum  should  be  made  sufficiently  longer  than 
the  combined  thickness  of  the  discs  to  allow  the  latter  to  separate 
completely  without  passing  beyond  the  rear  edge  of  the  rim. 


FIG.  24. — SKELETON   FORM   INNER  DRUM  AND  PRESSER. 


46 


FRICTION  CLUTCHES. 


Owing  to  the  fact  that  the  rirn  of  the  compressing  spider  must 
move  Over  the  rim  of  the  inner  drum  for  a  considerable  distance, 
while  at  the  same  time  the  web  ot  this  spider  must  be  quite 
close  to  the  web  of  the  inner  drum,  so  the  clutch  spring  will  not 
extend  too  far  to  the  rear  of  the  clutch  proper,  this  compression 
spider  usually  has  a  rather  awkward  form  and  is  quite  heavy. 
This  difficulty  can  be  overcome  by  making  the  inner  drum  in 
skeleton  form,  as  shown  in  Fig.  24,  cutting  away  its  rim  between 
those  portions  where  the  keyways  are,  and  making  the  compres- 
sion spider  spoked,  the  spokes  entering  between  the  lateral  projec- 
tions of  the  inner  drum  rim.  Besides  reducing  the  weight  of  the 
driven  part  of  the  clutch,  this  construction  allows  of  a  more 
compact  housing. 

Hele-S-haw  Clutch — A  special  type  of  multiple  disc  clutch 
which  is  extensively  used  both  in  this  country  and  abroad  is  the 
Hele-Shaw,  which  consists  of  alternate  discs  of  steel  and  phos- 
phor bronze  with  V-groove  corrugations  whose  walls  form  an 
angle  of  35  degrees.  Only  the  walls  of  the  V-grooves  come  in 
frictional  contact,  and  the  remaining  parts  of  the  discs  merely 
serve  to  help  radiate  the  heat  engendered  during  slippage.  Oil 
holes  are  drilled  through  the  inner  walls  of  the  grooves  near 
the  peak,  so  the  oil  can  enter  and  escape  freely.  It  is  obvious 
that  in  this  clutch  there  is  a  sort  of  wedge  action,  the  same  as 


r 


FIG.  25.— HELE-SHAW  CLUTCH. 


FRICTION  CLUTCHES. 


47 


FIG.  26.— CLUTCH  SPRINGS  INSIDE  SHAFT. 

in  a  cone  clutch,  and  much  less  spring  pressure  is  required  to 
produce  a  certain  amount  of  frictional  force  than  with  a  flat  disc 
clutch  of  the  same  number  of  discs  and  the  same  mean  diameter. 
On  the  other  hand,  the  discs  have  to  be  moved  laterally  consid- 
erably farther  to  obtain  the  proper  clearance  between  them,  and 
the  number  of  discs  that  can  be  used  is  therefore  more  limited. 
The  Hele-Shaw  clutch  shown  in  Fig.  25  is  provided  with  a  clutch 
brake,  as  are  most  large  size  disc  and  plate  clutches. 

Springs  Inside  of  Shaft — Generally  the  clutch  spring  sur- 
rounds the  clutch  shaft,  as  shown  in  Figs.  17,  18  and  19,  but  some 
designers  prefer  to  place  it  inside  the  clutch  shaft  or  the  engine 
tailshaft.  Two  such  designs  are  shown  in  Fig.  26.  In  the  first 
of  these  (Panhard)  the  spring  acts  through  a  plug  and  a  key 
which  extends  through  a  long  diametral  slot  in  the  shaft,  against 
the  clutch  compressing  spider.  In  the  second  (Hudson  "33") 
the  clutch  spring  is  located  inside  the  rear  bearing  of  the  crank- 
shaft and  presses  through  a  steel  washer,  a  collar  on  the  clutch 
shaft,  a  ball  thrust  bearing  and  a  screw  collar  against  the  hub  of 
the  inside  clutch  drum.  It  should  be  explained  that  in  this 
clutch  the  usual  order  of  things  is  reversed,  the  inner  drum 
being  moved  in  an  axial  direction  in  order  to  disengage  the 
clutch,  thus  serving  as  "presser." 


48  FRICTION  CLUTCHES. 

Lubrication  of  Discs — The  surfaces  of  the  discs  should  be 
covered  with  lubricant  when  there  is  slippage,  but  it  is  also  de- 
sirable that  all  or  at  least  most  of  the  lubricant  be  squeezed  out 
from  between  them  when  the  full  pressure  of  the  spring  is  ap- 
plied, since  the  clutch  will  hold  the  better  the  less  lubricant  there 
is  on  the  discs.  In  order  to  insure  these  conditions,  some  manu- 
facturers provide  the  discs  with  radial  slots  extending  over  half 
their  width,  as  shown  in 
Fig.  27,  through  which 
the  oil  may  escape  when 
the  discs  are  pressed  to- 
gether. 

Whereas  the  weak  point 

of     the      ordinary      cone  FIG.  27. — CLUTCH  Discs 

clutch  is  its  great  inertia,  WITH  OIL  SLOTS. 

that  of  the  multiple  disc- 

in-oil  clutch  is  its  tendency  to  drag  if  the  oil  in  the  clutch 
housing  is  not  suitable  for  the  purpose,  or  if  too  much  is  intro- 
duced. Most  makers  recommend  a  mixture  of  machine  oil  or 
gas  engine  oil  with  kerosene.  It  is  obvious  that  the  thinner  the 
lubricant  the  better  the  clutch  will  hold,  while  the  more  viscous 
the  lubricant  the  more  gradually  it  will  pick  up  its  load. 

Dry  Plate  Clutches— In  order  to  overcome  the  dragging  evil 
the  dry  plate  clutch  was  introduced.     In  this  one  set  of  plates 


FIG.  28. — CORK  INSERT  CLUTCH. 


FRICTION  CLUTCHES.  49 

is  either  faced  with  asbestos  fabric  on  both  sides  or  else  pro- 
vided with  cork  inserts.  Both  of  these  materials  when  in  contact 
with  steel  have  a  much  greater  friction  coefficient  than  steel  or 
bronze  on  steel.  Cork  on  steel  is  claimed  to  have  a  friction  co- 
efficient of  about  0.34  when  not  lubricated.  The  cork,  of  course, 
is  quite  compressible.  It  is  customary  to  make  the  plugs  of  such 
size  that  when  free  they  project  about  &  inch  above  the  sur- 
face of  the  metal  plate.  Hence  when  the  discs  are  forced  together 
the  contact  is1  at  first  between  metal  and  cork  only,  and  owing 
to  the  compressibility  of  the  cork  the  engagement  is  very  smooth. 
However,  when  the  full  pressure  of  the  spring  is  applied  to  the 
friction  surfaces  the  corks  are  compressed  flush  with  the  plate 
surface,  and  one  of  the  surfaces  is  then  part  metal  and  part  cork. 
This,  of  course,  will  reduce  the  effective  friction  coefficient  some- 
what, depending  upon  the  relative  area  of  the  corks  and  of  the 
metal  and  upon  the  compression  of  the  cork  at  the  moment  metal 
to  metal  contact  is  established.  As  a  rule,  the  cork  covers  from 
25  to  50  per  cent,  of  the  total  area  of  the  discs,  though  there  are 
extreme  cases  in  which  either  more  or  less  than  the  above  range 
is  covered. 

The  majority  of  disc  clutches  with  cork  inserts  are  of  the  three 
plate  type,  the  middle  plate  containing  the  corks,  though  occa- 
sionally cork  inserts  are  also  used  in  multiple  disc  clutches.  More- 
over, it  is  not  necessary  to  run  the  cork  insert  clutches  dry. 
Lubrication  will  reduce  wear  of  the  corks,  but,  of  course,  it  will 
also  reduce  the  friction  coefficient.  A  typical  cork  insert  clutch 
is  illustrated  in  Fig.  28. 

Asbestos  fabric  is  also  used  for  facing  clutch  discs.  This  is  a 
fabric  composed  very  largely  of  asbestos  fibre  and  containing 
some  brass  wire  and  cotton,  which  latter  give  the  necessary 
tenacity,  while  the  asbestos  is  used  on  account  of  its  good  fric- 
tional  qualities  and  its  resistance  to  heat.  The  asbestos  fabric  is 
secured  to  the  metal  discs  by  means  of  rivets  passing  through  the 
metal  and  asbestos  on  opposite  sides  of  it.  The  frictional  force 
in  asbestos-faced  disc  clutches  varies  from  less  than  one  pound 
to  about  four  pounds  per  square  inch.  With  lower  friction  per 
unit  surface  the  life  of  the  clutch  will,  of  course,  be  greater. 
The  friction  coefficient  of  asbestos  fabric  on  steel  seems  to  be 
approximately  0.3,  and  for  ordinary  purposes  a  normal  pres- 
sure of  10  pounds  per  square  inch  will  give  satisfactory  results. 
This  gives  a  frictional  force  of  three  pounds  per  square  inch,  and 


50  FRICTION   CLUTCHES. 

the  formulas  for  number  of  discs  and  spring  pressure  required 
become 

4T 


and 

/>==  I0  TT  (r02  —  n2)  .........................................  (14) 

From  the  data  at  hand  it  seems  that  these  same  equations  are 
applicable  to  cork  insert  clutches  in  which  the  spring  acts 
on  the  discs  directly  and  in  which  the  corks  cover1  from  25  to  50 
per  cent,  of  the  total  surface. 

It  may  here  be  pointed  out  that  a  clutch  for  a  vehicle  in  which 
the  gear  has  to  be  changed  frequently  and  the  clutch  therefore 
slipped  a  great  deal  should  logically  be  designed  with  a  somewhat 
lower  unit  friction  force  than  a  clutch  for  a  high  powered  touring 
car,  for  instance,  the  speed  of  which  can  be  largely  controlled  by 
the  throttle.  A  lower  unit  frictional  force  will  result  in  less 
wear  and  less  heating. 

The  asbestos  is  generally  secured  to  the  driving  discs,  so 
the  driven  member  may  have  the  least  possible  inertia,  but  in 
one  design  the  asbestos  rings  are  free  between  the  two  sets  of 
metal  discs.  The  latter  are  made  about  %  inch  thick  to  get 
sufficient  bearing  surface  on  the  keys  ;  if  lighter  stock  is  to  be 
used  the  edges  may  be  flanged  to  get  additional  driving  area. 
Fig.  29  shows  the  Packard  dry  disc  clutch  which  comprises 
six  driving  and  five  driven  discs. 

Three  Plate  Clutches  —  Another  method  of  obviating  the 
dragging  tendency  of  disc  clutches  is  to  use  only  three  discs  or 
plates,  without  lubricant.  These  discs  are  made  of  cast  iron 
and  bronze,  or  of  cast  iron  and  steel.  Since  there  are  only 
two  friction  surfaces,  for  moderately  high  powers  it  is  necessary 
to  use  rather  large  discs  and  to  multiply  the  pressure  of  the  clutch 
spring  by  levers  or  toggle  mechanisms.  Fig.  30  shows  a  typical 
design  of  this  kind  in  which  the  spring  pressure  is  multiplied  by  a 
toggle  mechanism.  One  of  the  three  discs  is  a  driving  disc,  and 
the  other  two  are  driven  discs.  The  driving  disc  is  driven  from 
the  flywheel  through  keys  riveted  to  the  inside  of  the  flywheel 
rim.  One  of  the  driven  discs,  the  one  nearest  the  flywheel,  is 
secured  to  the  clutch  shaft  and  is  provided  with  four  sets  of 
laterally  extending  lugs  on  which  bell  cranks  are  fulcrumed.  One 
arm  of  these  bell  cranks  connects  through  a  link  with  a  sliding 
sleeve  on  the  clutch  shaft  on  which  the  clutch  spring  acts.  The 
other  arm  of  the  bell  crank  is  provided  with  a  set  screw,  the 
point  of  which  presses  against  the  rearmost  driven  disc.  This 
latter  disc  is  provided  with  driving  lugs  which  enter  between  the 


FRICTION  CLUTCHES 


52 


FRICTION  CLUTCHES. 


lugs  on  the  other  disc  serving  as  a  fulcrum  for  the  bell  crank. 
The  set  screws  permit  of  making  adjustment  for  wear  of  the 
discs.  Separation  of  the  discs  is  effected  by  means  of  small  coiled 
springs  inserted  into  drill  holes  in  one  of  the  driven  discs  and 
pressing  against  the  other  driven  disc. 

The  multiplying  factor  of  the  toggle  mechanism   attains  the 
infinite  as  the  toggles  assume  a  radial  position.     In  practice,  of 


FIG.  30.— THREE  PLATE  TOGGLE  TYPE  CLUTCH. 


course,  the  set  screws  must  be  so  adjusted  that  this  cannot  hap- 
pen, as  the  toggle  links  would  pass  by  the  radial  position  and  the 
clutch  would  disengage  again.  If  the  links  make  a  small  angle  0 
with  a  radial  line  then  the  multiplying  factor  is  equal  to  co- 
tangent 0.  This  may  be  readily  seen  by  reference  to  Fig.  31,  in 


FRICTION   CLUTCHES. 


53 


which  A  B  represents  a  link  of  the  toggle.  Let  P  be  the  pres- 
sure of  the  spring  and  N  the  radial  pressure  exerted  on  the  bell 
crank  arm.  Now  let  point  B  be  moved  the  slightest  distance 
under  the  force  of  the  spring  P,  so  that  the  angle  B  A  C  (0) 
decreases  to  0  —  d  0.  Now  we  have 

C  B  =  A  B  sin  0 
A  C  =  A  C  cos  0 
When  0  decreases  to  0  —  d  <t>, 
A  B  sin  0  decreases  by  A  B 
cos  0  d  0  and  A  B  cos  0  in- 
creases by  A  B  sin  0  d  <f>.  But 
the  product  of  the  force  into 
the  distance  through  which  it 
works  represents  the  work 
done,  and  this  must  be  the 
same  at  both  points  A  and  B. 
Hence, 

PX  A  £  cos  <j>  d  <j>  = 


N X  ABsin<t>d$ 


and 


*L 
p 


cos  0 


FIG.  31. 


sin  0 " 

A  plate  clutch  in  which  the 
spring  pressure  is  multiplied 
by  double  armed  levers  is  illustrated  in  Fig.  32.  In  this  clutch  there 
are  two  driving  discs,  one  being  constituted  by  the  web  of  the 
flywheel,  and  one  driven  disc.  The  free  driving  disc  is  driven 
from  the  flywheel  through  a  stud  bolt  passing  through  the  fly- 
wheel web  and  an  annular  flange  bolted  to  the  flywheel  rim.  The 
stud  bolt  is  provided  with  a  collar  against  which  the  short  arm 
of  the  double  armed  lever  takes  purchase.  This  lever  is  fulcrumed 
on  lugs  cast  integral  with  the  free  driving  plate,  and  its  long 
arm  extends  radially  inward  and  is  pressed  against  by  the  sliding 
sleeve  which  contains  the  clutch  spring  and  is  formed  with  the 
groove  or  flange  for  the  shipping  collar. 

Band  Clutches— Band  clutches  are  of  two  kinds,  viz.,  con- 
tracting and  expanding.  A  contracting  band  clutch  consists  of 
a  drum  and  a  metal  band  surrounding  it,  which  may  be  lined 
with  friction  material.  One  end  of  the  band  is  fixed  to  a  spider 
or  housing  carried  upon  one  of  the  connected  shafts,  and  the 
other  end  can  be  displaced  angularly  with  relation  to  the  first 
so  as  to  contract  the  band  into  frictional  contact  with  the  drum. 
Contracting  band  clutches  are  of  three  different  types.  The 


54 


FRICTION  CLUTCHES. 


first  of  these,  shown  in  Fig.  33,  comprises  two  bands  of  which 
each  extends  substantially  half  way  around  the  circumference 
of  the  clutch  drum.  The  bands  are  generally  made  from  thin 
strip  steel,  and  lined  with  leather.  One  end  of  each  band  is 
hinged  to  one  arm  of  a  two  armed  spider  secured  to  the  driven 
shaft  or  clutch  shaft,  and  the  other  end  to  the  short  arm  of 
a  double  armed  lever  fulcrumed  on  the  arm  of  the  spider,  the 


FIG.  32. — PLATE  CLUTCH,  LEVER  TYPE. 

inwardly  extending  arm  of  the  lever  being  adapted  to  be  moved 
outward  from  the  clutch  axis  by  a  sliding  cone  or  wedge  under 
the  pressure  of  the  clutch  spring.  When  the  levers  are  thus 
moved  around  their  fulcra  the  bands  are  drawn  tight  on  the 
clutch  drum,  and  driving  connection  is  established. 


FRICTION  CLUTCHES. 


55 


56 


FRICTION  CLUTCHES. 


Fig.  34  shows  the  Mercedes  coil  clutch,  which  may  also  be 
regarded  as  a  form  of  band  clutch.  The  band  in  this  case  con- 
sists of  a  coil  of  steel,  one  end  of  which  is  anchored  to  the  hous- 
ing of  the  clutch  and  the  other  end  of  which  is  attached  to  one 
arm  of  a  double  armed  lever  whose  fulcrum  support  is  in  the 
end  wall  of  the  housing.  The  long  arm  of  this  lever  is  acted 
upon  by  a  sliding  cone  against  which  the  clutch  spring  presses. 
When  the  sliding  cone  is  forced  under  the  lever  arm  the  steel 
coil  is  contracted  upon  the  clutch  drum  and  grips  the  latter.  The 


FIG.  34. — 'MERCEDES  COIL  CLUTCH. 


housing  is  formed  integral  with  the  flywheel  and  the  drum  is  se- 
cured to  the  clutch  shaft.  This  clutch  is  entirely  enclosed  and 
runs  in  oil. 

Theory  of  Band  Clutch — In  Fig.  35  is  shown  a  sketch 
of  a  band  clutch  in  which  d9  represents  a  small  arc  of  con- 
tact of  the  band  on  the  drum  and  6  the  angle  or  arc  of  contact 
between  this  section  dO  and  the  point  of  contact  between  band 
and  drum  nearest  to  the  free  end  of  the  band.  At  the  free  end 
a  pull  Pi  is  exerted  on  the  band.  Owing  to  the  friction  between 


FRICTION  CLUTCHES. 


57 


the  band  and  drum  the  pull  on  the  band  varies  from  point  to  point 
of  its  length.  Let  the  pull  at  one  side  of  the  differential  section 
d  0  be  represented  by  P  and  that  on  the  other  side  by  P  +  d  P, 
as  indicated  in  the  sketch.  Also  let  the  normal  pressure  between 
the  band  and  drum  on  the  section  d  0  be  represented  by  N  and  the 
f rictional  force  resulting  therefrom  by  /  N.  When  the.  system  is 
in  equilibrium  the  forces  in  any  direction  are  equal  to  zero. 
Hence,  taking  the  forces  in  the  horizontal  plane, 
dd  d8 

(P  +  dP)cos-    -fN  —  Pcos—  =  O 

2  2 

But  the  cosine  of  an   infinitely  small  angle   is   equal  to  unity, 
hence 
dP  =  fN (15) 


FIG.  35.  —  DIAGRAM  OF  BAND  CLUTCH. 
Now,  taking  the  forces  in  the  vertical  plane, 

dO  d6 

N  —  (P  +  d  P)  sin  --  P  sin  —  =  O 

and  since  the  sine  of  an  infinitely  small  angle  is  equal  to  the 
arc,  we  may  write  $0  je 

N  —  (P  +  d  P)  --  P  —  =  O 
2  2 

do 


The    term    d    P  —  ,    a    differential    expression    of    the    second 

2 

order,  may  be  neglected,  and  we  may  write 
N  =  P  d  0 


58  FRICTION  CLUTCHES. 

or 

AT 

=  7* ; (16) 

Dividing  equation  (15)  by  equation  (16)  we  get 
dP 

=  f  d  e 

dX 
Now  the  integral  of  a  differential  expression  of  the  form  

x 
is  log  x   (the  natural  logarithm,  whose  base  is  2.71828.     Hence 

log  P  =  /  0  +  C 
or 

log  P  =  /  0  4-  log  c (17) 

Remembering  that  in  all  logarithmic  systems  the  logarithm  of  the 
base  is  1,  we  may  write 

log  e*  0  =  fO  X  1  =fO 
Inserting  this  value  of  /  6  in  equation  (17)  we  have 

log  P  =  log  ef  0  +  log  c 
and  taking  antilogs — 
P  =  c  e<  e (18) 

To  find  the  value  of  the  constant  c  we  make  0  equal  to  zero, 
in  which  case  P  equals  the  initial  pull  Pi  applied  to  the  free 
end  of  the  band. 

Pi  =  c  e°. 
But  any  term  with  the  exponent  zero  is  equal  to  unity,  hence 

C    =   Ft 

and  inserting  this  value  in  equation   (18)   we  have 

P  =  Pi  ef  0 (19) 

This  latter  equation  gives  the  pull  on  the  band  at  any  angle  6 
from  the  point  of  contact  between  band  and  drum  nearest  the 
point  of  application  of  the  initial  pull.  The  total  frictional  force 
F  between  the  band  and  drum  is  equal  to  the  difference  be- 
tween the  initial  pull  and  the  pull  at  the  point  of  contact  between 
band  and  drum  farthest  from  the  point  of  application  of  the 
initial  pull — 

F  =  P,  ef  e  —  P,  =  P,  (ef  0  —  1) 
and 

P1  =  — — (20) 

efe—i 

In  using  this  equation  the  arc  0  must  be  expressed  in  radians. 
Values  of  the  expression  ef  &  —  1  for  various  values  of  /  9  may  be 
found  from  Fig.  36. 


FRICTION  CLUTCHES. 

59 

«/?/- 

£.0  20 

l.Q     16 
1.6     16 
14     H 
1.2    12. 
1.0     1O 
0.6     6 
O.G      6 
0.4    4 
0.2    2 

0 

- 

/ 

/ 

/ 

/ 

y 

./ 

/ 

/ 

/ 

/ 

/ 

d 

/ 

/ 

c 

,y 

/ 

^ 

^ 

/ 

& 

? 

/ 

r 

/ 

A 

/ 

/ 

fr 

c 
tfl 

/ 

y 

* 

r 

^ 

^ 

tf 

y 

x1 

./* 

/ 

X 

^ 

/ 

^ 

^ 

' 

a* 

"•"' 

*** 

r          LZ         1.4       1C         1.6         Z         22       2*       Z.6       2.<3       3 
J              0£              O7              0.8              09              1.0             U 

Value  of  /e 

FIG.  36. — CURVE  GIVING  RATIO  BETWEEN  FRICTIONAL  FORCE  AND 

PULL  ON  BAND. 

Sample  Calculation— Now  let  it  be  required  to  design  a  band 
clutch  for  a  four  cylinder  4x5  inch  motor,  which,  as  we  have 
seen,  develops  a  torque  of  133  pounds-feet.  Suppose  we  choose 
a  drum  12  inches  in  diameter,  then  the  frictional  force  required 
at  the  surface  of  the  drum  is 

133  X  I2  =  266 founds. 
6 

Let  the  band  be  made  of  steel  and  lined  with  leather,  so  we 
can  figure  on  a  coefficient  of  friction  f  =  o.2.  In  the  case  of  a 
clutch  comprising  a  band  extending  all  around  the  drum  the  arc 
of  contact  will  be  about  5.5  radians,  and  in  the  case  of  a  clutch 
with  two  bands,  each  extending  half  way  around  the  drum,  the 
arc  of  contact  of  each  will  be  about  2.5  radians.  These  figures 
are  approximate  and  the  correct  arcs  of  contact  would  have  to 
be  determined  from  the  drawings. 

Let  us  take  the  case  ot  a  single  band  brake.  Inserting  values 
in  equation  (20)  we  have 


60  FRICTION  CLUTCHES. 


This  is  the  pull  which  must  be  exerted  on  the  free  end  of  the 
band.  The  pull  of  the  fixed  end  on  its  anchorage  is  equal  to  the 
pull  on  the  free  end  plus  the  friction, 

133  +  266  =  399  pounds, 

and  the  band  and  its  anchorage  must  be  designed  sufficiently 
strong  to  withstand  this  stress. 

If  the  band  is  of  uniform  width  the  normal  pressure  at  its 
contact  surface  varies  from  end  to  end,  being  least  near  the  free 
end  and  most  near  the  fixed  end.  From  equation  (16)  it  will  be 
seen  that  N  varies  directly  as  the  pull  P  on  the  band.  We  know 
that  the  f  rictional  force  F  =  266  pounds,  and  since  the  coefficient 
of  friction  is  0.2,  the  aggregate  normal  pressure  is 

OAA 

Q  2    =  1,330  pounds. 

Also,  if  we  allow  an  average  unit  pressure  of  18  pounds  per 
square  inch,  then  the  frictional  area  required  is 

1,330 
—  jg—    =  74  square  inches, 

and  since  the  drum  has  a  diameter  of  12  inches,  and  consequently 
a  circumference  of  37.68  inches,  it  would  have  a  width  of 

3;  53  =  2  inches  (appr.) 

The  normal  pressure,  as  already  stated,  will  not  be  uniform  but 
greater  near  the  fixed  end  than  near  the  free  end  in  the  propor- 
tion of  399  :  133  or  3  to  1.  Hence  the  lining  will  wear  faster 
near  the  fixed  end. 

Effect  of  Centrifugal  Force  —  At  high  "speeds,  like  those  em- 
ployed in  automobile  clutches,  the  centrifugal  force  on  the  band 
h:,s  quite  an  effect  on  the  friction  between  the  band  and  the  drum, 
and  this  is  the  cause  of  the  chief  difference  between  a  contracting 
band  clutch  and  an  expanding  band  clutch.  The  above  analysis 
with  respect  to  the  frictional  force  between  band  and  drum 
at  low  speeds  applies  equally  to  both  types  of  band  clutches,  but 
the  centrifugal  force  tends  to  expand  the  band,  and  hence  to 
decrease  the  frictional  force  of  a  contracting  clutch,  and  to  in- 
crease the  frictional  force  of  an  expanding  clutch. 

Let  w  be  the  weight  of  a  section  of  the  band  1  inch  in  length. 
Then  the  weight  of  an  element  d  &  of  the  band  is  w  r  d  Q  and  the 
centrifugal  force  on  this  element  (see  equation  31,  Vol.  1)  is 

1.226  (iv  rdB)1r  —  =  0.102  w  if  r*  d  e, 


FRICTION   CLUTCHES.  61 

where  w  is  the  speed  in  revolutions  per  second  and  r  the  radius 
in  inches.  This  force,  which  we  will  denote  by  Fc  d  0  (Fc  being  the 
centrifugal  force  on  a  section  of  the  band  equal  to  one  radian), 
in  a  contracting  clutch  acts  in  the  same  direction  as  force  N. 
Hence  we  may  write  the  equation  of  the  forces  in  the  vertical 
plane  — 


Transposing  and  contracting, 

(P  —  Fc) 
and 


But  since  Fc  is  constant, 

d  (P  —  Fc)  =dP  =  f  N  (equation    15). 
Hence 


Integrating  both  sides  of  the  equation, 

log  (P  — Fc)  =f  0  +  C  =  f  0+  log  a 
and  taking  antilogs  — 

P—  Fc-=ae*d 

In  order  to  determine  the  constant  for  this  case,  let  0  =  o,  then 
P  =  Pi,  and 

hence 

and 

j?=  P pl  =  (Pl  —  Fc)  e*  6  -{-  Fc  —  PI 

Multiplying  out, 


Transposing 

and  dividing  by  the  coefficient  of  Pi, 


Comparing  equation  (21)  with  equation  (20)  we  see  that  the 
effect  of  the  centrifugal  force  on  the  band  of  a  contracting  clutch 
is  to  increase  the  required  pull  on  the  free  end  of  the  band  by  an 
amount  equal  to  the  centrifugal  force  on  a  section  of  the  band 
one  radian  in  length.  This  might  have  been  expected,  since  the 
total  centrifugal  force  on  the  band  is  2irFc,  and  if  the  band 


62  FRICTION  CLUTCHES. 

moves  radially  outward  under  this  force  a  distance  x,  then  the 
free  end  of  the  band  will  be  moved  a  distance  2  •*  x.  Hence  the 
motion  of  the  free  end  is  2  TT  times  greater  than  the  radial  mo- 
tion, and  the  force  in  the  direction  of  motion  of  the  free  end 
2  v  times  smaller  than  the  radial  (centrifugal)  force. 

Equation  (21)  is  applicable  to  contracting  band  clutches  at  all 
speeds.  A  similar  analysis  may  be  applied  to  expanding  band 
clutches,  and  the  resulting  equation  for  the  initial  pull  required 
is  the  same  as  (21),  except  that  the  sign  of  the  term  Fc  is 
reversed,  the  centrifugal  force  in  this  case  adding  to  the  normal 
pressure,  instead  of  subtracting  from  it.  Therefore,  for  expand- 
ing clutches — 

F 

P>  =  —  Fc  (22) 

e'0-1 

Returning  to  the  examples  of  a  band  clutch  for  a  motor  devel- 
oping a  torque -of  133  pounds-feet,  let  the  band  weigh  0.1  pound 
per  inch  of  length ;  then 

Fc  =  0.102  X  0.1  X  202  X  62  =  147  pounds 
the  initial  pull  becomes 

p*  =  3?IT+  147  =  28°  Pounds, 
and  the  pull  at  the  anchorage  of  the  band  is 

280  +  266  =  546  pounds. 

Expanding  Band  Clutches — Expanding  band  clutches  of  the 
type  shown  in  Fig.  37  require  comparatively  little  pressure  to 
hold  them  in  engagement  at  high  speed,  since  the  centrifugal 
force  on  the  band  presses  it  against  the  inside  of  the  clutch 
drum.  The  advantage  of  this  fact  is  doubtful,  however,  since 
the  greatest  torque  is  produced  by  the  motor — and,  conse- 
quently, the  greatest  frictional  force  required  of  the  clutch — 
at  low  motor  speed.  If  in  this  type  of  clutch  the  spring 
were  to  act  against  a  sliding  cone,  which  through  a  connecting 
linkage  acted  on  the  free  end  of  the  band,  the  latter  at  high 
speed  would  not  be  released  from  the  drum  when  the  sliding 
cone  was  withdrawn,  owing  to  the  fact  that  the  centrifugal 
force  on  the  band  would  then  produce  the  necessary  fric- 
tional force  betwen  band  and  cone  to  hold  the  load.  Conse- 
quently, the  operating  mechanism  must  be  so  arranged  that 
when  the  sliding  sleeve  is  moved  by  pressing  on  the  clutch 
pedal  the  band  is  positively  released  from  the  drum.  The 
band  rs  made  of  band  steel,  faced  with  leather,  and  supported 
by  a  skeleton  drum  which  can  be  cast  of  aluminum,  or  the  band 
may  be  made  of  a  ribbed  iron  casting  yieldingly  supported 


FRICTION  CLUTCHES. 


63 


by  a  bracket.  The  engaging  pressure  is  furnished  by  a 
tension  spring,  whose  one  end  is  anchored  to  the  web  of 
the  band  supporting  drum.  In  some  designs  a  second  spring 
must  be  provided  to  keep  the  sliding  cone  in  contact  with  the 
operating  lever,  which  spring  may  either  surround  the  clutch 
shaft  and  press  directly  against  the  cone,  or  may  be  anchored 
to  some  part  of  the  car  frame  and  draw  the  clutch  pedal  in 
the  direction  corresponding  to  clutch  engagement. 

In  another  type  of  band  clutch  both  ends  of  the  band  are 
free  and  the  middle  is  anchored  to  a  bracket  on  the  driving 
shaft.  In  this  case  one-half  of  the  band  is  drawn  tighter  on 


FIG.  37.— EXPANDING  BAND  CLUTCH. 

the  drum  by  the  friction  between  band  and  drum,  and  the 
other  half  is  unwound,  as  it  were.  Hence  the  effects  of  the 
friction  on  the  pull  or  tension  in  the  halves  of  the  band 
exactly  neutralize  each  other  and  can  be  neglected  in  cal- 
culating the  frictional  force.  Let  P  be  the  pull  exerted  on 
each  free  end  of  the  band,  and  suppose  that  under  this  pres- 
sure the  ends  move  together  a  distance  x.  Then,  if  the  band 
is  supposed  to  be  of  circular  shape,  both  before  and  after 


64 


FRICTION  CLUTCHES. 


FRICTION   CLUTCHES.  65 

the  contraction,  the  radius  will  be  reduced  by  —  •      Since  the 

27T 

ratio  of  circumferential  to  radial  motion  is  2  ^  the  ratio  of 
circumferential  to  radial  pressure  is  —  and  the  total  normal 

2  IT 

pressure  is  2-rrP,  which  when  multiplied  by  the  coefficient  of 
friction  gives  the  total  frictional  force. 

Expanding  Block  Clutches  —  This  type  of  clutch,  which  is 
widely  used  in  stationary  work,  is  rarely  found  in  automobile 
practice.  It  consists  of  a  drum  and  two  or  more  blocks  or 
segments  which  by  means  of  toggles  or  right  and  left  hand 
screws  can  be  expanded  against  the  rim  of  the  drum.  The 
blocks  are  in  driving  connection  with  a  spider  secured  to 
the  clutch  shaft.  The  calculation  of  such  a  clutch  is  very 
simple.  From  the  arrangement  of  the  mechanism  the  multipli- 
cation of  the  spring  pressure  at  the  friction  surface  can  be 
readily  calculated  and  the  frictional  force  is  then  equal  to 
the  product  of  the  normal  pressure  by  the  friction  coefficient. 
These  blocks  or  segments  are  often  faced  with  fibre  or  leather. 
though  they  may  also  have  metallic  surfaces.  The  Metallurgique 
clutch,  a  typical  expanding  segment  clutch  with  right  and  left 
hand  screw  operating  mechanism,  is  shown  in  Fig.  38.  In  the 
Mais  truck  clutch,  the  clutch  surface,  instead  of  being  a  cyl- 
indrical envelope,  is  corrugated,  so  as  to  increase  the  normal 
pressure  on  the  frictional  surface  on  the  principle  of  a  wedge. 

Clutch  Shaft  Dimensions  —  The  torsional  strength  of  shafts 
is  calculated  by  means  of  the  formula 
M  =  0.196  d3  S, 

where  M  is  the  torsional  moment  in  pounds-inches,  d  the 
diameter  of  the  shaft  .in  inches,  and  5"  the  safe  torsional  stress 
in  pounds  per  square  inch.  6"  can  be  figured  at  5,000  pounds  per 
square  inch  for  carbon  steel  and  7,000  pounds  for  nickel  and 
chrome-nickel  steel.  The  torsional  moment  of  a  four  cylinder 
4x5  inch  engine  would  be 

12  x  133  =  1,596  pounds-inches. 
Hence 

0.196  d*x  5,000=  1,596 
and 


d=\/  -       ?  -  =  1.18  —  say  i  T3s  inch, 

r    0.196  X  5000 
for  carbon  steel. 

Of  course,  if  the  shaft  is  weakened  in  any  way,  as  by  being 
squared  for  a  coupling,  the  diameter  should  be  made  propor- 
tionally heavier.  The  stress  allowed  in  the  shaft  seems  to  be 


66 


FRICTION   CLUTCHES. 


very  low,  bat  a  high  factor  of  safety  is  necessary,  since,  owing 
to  changes  in  the  coefficient  of  friction  of  the  clutch  facing  and 
adjustment  of  the  spring  pressure,  the  torque  transmitting  ca- 
pacity of  the  clutch  may  be  greatly  increased  and  much  greater 
torques  than  that  of  which  the  engine  is  capable  continuously 
may  be  produced  by  "jamming  in"  the  clutch  while  the  engine 
is  racing,  thus  withdrawing  some  of  the  energy  stored  up  in 
the  flywheel.  All  other  parts  of  the  clutch  transmitting  the 
torque  of  the  motor  should  be  calculated  on  the  same  basis, 
allowing  a  factor  of  safety  of  about  10. 

In  these  calculations,  as  well  as  in  the  calculations  of  other 
transmission   members,   unless    exceptions    are    specifically   men- 


FIG.  39. — BLOCK  AND  TRUNNION  TYPE  UNIVERSAL  AND  SLIP  JOINT. 

tioned,  a  torque  based  upon  a  brake  mean  effective  pressure  of 
80  pounds  per  square  inch  is  to  be  used.  That  is  to  say,  the 
constants  of  all  formulae  to  be  given  will  be  based  on  this  engine 
torque,  which  may  be  found  from  Chart  I. 

Connection  Between  Clutch  and  Change  Gear — In  a  cone 
clutch  the  torque  of  the  motor  is  transmitted  by  the  cone  and 
the  hollow  shaft  to  which  it  is  secured,  and  since  the  cone  must 
move  in  an  axial  direction  when  it  is  engaged  and  disengaged, 
there  must  of  necessity  be  a  slip  joint  in  the  transmission  line 
between  the  clutch  and  the  change  gear.  The  same  applies  to 
some  other  types  of  clutches,  as,  for  instance,  multiple  disc 
clutches  in  which  the  inner  drum  serves  also  as  the  presser. 
Moreover,  unless  the  change  gear  housing  and  engine  crank  case 
are  rigidly  secured  together,  it  is  very  desirable  that  a  double 
universal  joint  be  interposed  between  clutch  and  change  gear,  so 
there  may  be  no  binding  of  the  bearings  of  either  member  when 
the  vehicle  frame  "weaves"  or  distorts  in  consequence  of  road 
shocks,  and  also  so  as  to  obviate  the  necessity  of  absolute  align- 
ment in  assembling.  A  favorite  construction  of  universal  and 


FRICTION  CLUTCHES. 


67 


slip  joint  in  connection  with  cone  clutches  is  the  block  and  trun- 
nion type  illustrated  in  Fig.  39.  The  shaft  is  forged  with  a 
transverse  hub  which  is  drilled  to  receive  a  trunnion.  Over  this 
trunnion  are  slipped  two  square  blocks  of  steel,  adapted  to  slide 
lengthwise  in  slots  formed  on  the  inside  of  the  hollow  shaft. 
These  slots  may  be  cut  in  a  planer  or  shaper  in  a  short  length 
of  hollow  shaft  which  is  flange-bolted  to  the  adjacent  trans- 
mission part,  or  the  slots  may  be  milled  entirely  through  the  wall 
of  the  hollow  shaft,  for  a  certain  distance  from  the  end,  and  a 
piece  of  steel  tubing  forced  over  the  end  of  the  shaft  as  far  as 
the  slots  extend. 

In  calculating  the  necessary  size  of  the  blocks  and  trunnions 
a  unit  pressure  of  1,200  pounds  per  square  inch  can  be  figured 


FIG.  40.— INTERNAL  AND  SPUR  GEAR  TYPE  OF  UNIVERSAL  AND 
SLIP  JOINT. 

on  between  the  blocks  and  the  walls  of  the  slots  in  which  they 
slide,  and  a  unit  pressure  of  1,800  to  2,000  pounds  per  square  inch 
between  the  trunnions  and  the  blocks.  In  order  to  obtain  the 
maximum  bearing  surface  with  a  given  outside  diameter  of  hol- 
low shaft,  the  blocks  are  often  beveled  off  on  the  outside  and 
beveled  out  on  the  inside.  These  blocks  are  hardened  and  the 
hollow  shafts  case  hardened,  to  reduce  wear.  To  obviate  rattling 
of  the  intermediate  shaft  against  the  ends  of  the  hollow  shaft,  a 
spring  is  sometimes  placed  between  one  of  the  hollow  shafts  and 
the  intermediate  shaft,  which  takes  up  the  end  play.  Another 
method  of  accomplishing  the  same  result  consists  in  using  a 
standard  form  of  universal  joint  at  one  end  of  the  short  inter- 
mediate shaft  and  a  block  and  trunnion  type  of  joint  at  the 
other.  The  block  and  trunnion  type  of  joint  must  be  packed  in 


68  FRICTION   CLUTCHES. 

grease,  and  to  this  end  must  be  provided  with  a  leather  "boot,  as 
shown  in  Fig.  39. 

Another  type  of  universal  and  sliding  joint  employed  between 
clutch  and  change  gear  consists  of  spur  and  internal  gears.  A 
design  of  this  kind  is  used  on  the  Oldsmobile,  and  is  illustrated 
in  Fig.  40.  The  intermediate  shaft  is  forged  with  flanges  at 
both  ends  which  are  cut  with  spur  teeth  on  their  circumference. 
These  teeth  mesh  with  the  teeth  of  internal  gears  bolted  re- 
spectively to  the  clutch  shaft  and  a  coupling  fixed  to  the  change 
gear  driving  shaft.  Since  the  two  sets  of  gears  do  not  run 
together  it  is  not  necessary  that  their  teeth  should  be  of  any 
particular  form,  and  substantially  square  teeth  probably  are  the 
most  advantageous.  Leather  discs  bolted  to  the  sides  of  the  two 
gears  respectively  here  take  the  place  of  the  usual  leather  boots, 
and  at  the  same  time  limit  the  endwise  play  of  the  intermediate 
shaft  and  thus  prevent  rattling. 

Leather  disc  universals  are  also  much  used  between  the  clutch 
and  transmission.  These  are  discussed  in  the  chapter  on  Uni- 
versal joints. 

End  Thrust  Due  to  Pedal  Pressure. — Most  modern  auto- 
mobile clutches  are  so  designed  that  when  they  are  engaged 
the  spring  pressure  is  self-contained.  However,  when  the  clutch 
is  disengaged  the  end  thrust  due  to  the  pressure  on  the  clutch 
pedal  has  to  be  taken  up  in  some  way.  The  clutch  itself  is  not 
supported  by  any  structural  part,  and  this  thrust  may  be  trans- 
mitted either  to  the  engine  crankshaft  or  to  the  driving  shaft 
of  the  change  speed  gear,  whichever  seems  the  most  convenient 
and  practical  in  any  particular  design.  Another  thing  to  be  con- 
sidered is  the  possibility  of  dismounting  the  clutch  without  re- 
moving the  engine  or  gear  box — especially  those  clutches  vith 
renewable  wearing  surfaces. 


CHAPTER  III. 


SLIDING  CHANGE   SPEED   GEARS. 

Historical — Many  different  devices  have  been  tried  for 
changing  the  gear  ratio  between  the  motor  and  the  driving 
wheels  of  an  automobile,  and  the  change  gear  was  long  thought 
to  present  the  most  difficult  problem  in  automobile  design. 
Daimler  and  Benz,  the  pioneers  of  the  gasoline  automobile,  both 
used  belts  and  stepped  pulleys  in  their  earliest  designs.  The 
Daimler  motor  was  taken  up  in  France  by  the  firm  of  Panhard 
&  Levassor,  and  after  a  few  experiments  with  belts  M.  Levassor, 
the  engineer  of  the  concern,  introduced  the  sliding  pinion  change 
speed  gear  in  combination  with  the  leather  faced  cone  clutch. 
The  idea  of  meshing  toothed  gears  by  shifting  them  axially 
was  at  first  ridiculed  as  crude  and  unmechanical,  but  in  the 
end  the  system,  after  having  undergone  a  number  of  important 
refinements  and  modifications,  proved  more  satisfactory  on  the 
whole  than  all  others,  and  it  is  now  in  almost  universal  use. 

Levassor's  change  gear  is  illustrated  in  Fig.  41.  It  con- 
sists of  two  parallel  shafts  mounted  in  bearings  in  an  alumi- 
num gear  box.  The  first  of  these  shafts,  known  as  the  pri- 
mary shaft,  is  in  driving  connection  with  the  clutch.  This 
shaft  is  squared  and  carries  a  set  of  three  toothed  gears  or 
pinions,  whose  common  hub  has  a  square  hole  broached  through 
it  to  make  a  sliding  fit  with  the  square  shaft.  On  the 
secondary  shaft  are  carried  three  other  toothed  gears,  each 
of  such  a  diameter  as  to  properly  mesh  with  one  of  the  gears 
on  the  primary  shaft.  The  gears  on  both  shafts  are  so 
spaced  that  by  shifting  the  primary  set  corresponding  gears 
on  the  two  shafts  can  be  brought  in  to  mesh  successively  with- 
out interference  from  the  other  gears.  Shifting  of  the  sliding 
set  is  accomplished  by  means  of  a  hand  lever  located  con- 
venient to v  the  operator,  and  a  suitable  connecting  linkage. 
The  secondary  shaft  at  its  rear  end  carries  a  bevel  pinion 
meshing  with  a  bevel  gear  on  a  cross  shaft  or  jackshaft,  from 

69 


70 


SLIDING   CHANGE   SPEED    GEARS. 


which  the  power  is  transmitted  to  the  rear  wheels  by  means 
of  side  chains. 

One  disadvantage  of  Levassor's  gear  set  was  that  the 
power  was  transmitted  through  a  pair  of  toothed  gears — with 
consequent  power  loss,  noise  and  wear — even  at  high  car 
speeds,  when  there  was  absolutely  no  occasion  for  it,  since 
the  speed  was  not  changed  by  the  gearing.  This  objection 
was  overcome  in  a  change  gear  brought  out  some  years 
later  by  Louis  Renault,  which  differed  from  Levassor's  in 
that  the  gears  of  the  two  shafts  were  rolled  into  mesh  instead 


FIG.  41. — SKETCH  OF  LEVASSOR'S  SLIDING  CHANGE  SPEED  GEAR 

of  being  slid  into  mesh.  The  primary  shaft  of  this  gear  set 
was  in  two  parts,  the  forward  or  driving  part,  and  the  rear- 
ward or  driven  part,  the  latter  being  journaled  at  its  forward 
end  inside  the  former.  The  secondary  shaft  served  as  a 
countershaft  through  which  the  motion  was  transmitted  for 
low  and  intermediate  speed  and  for  reversing.  For  high 
speed  the  two  parts  of  the  primary  shaft  were  locked  together 
by  means  of  jaw  clutches  formed  integral  with  gears  on  the 
two  parts  of  the  primary  shaft,  which  could  be  slid  into  en- 
gagement. This  gave  the  so-called  direct  drive,  the  power 
being  carried  directly  through  the  gear  set  without  being 
transmitted  through  the  toothed  gears.  The  direct  drive  fea- 
ture was  soon  also  incorporated  in  the  Levassor  type  of  slid- 


SLIDING  CHANGE  SPEED  GEARS. 


71 


ing  gear,  as  shown  in  Fig.  42.  This  gear,  which  is  known  as 
the  three  speed  and  reverse  progressive  sliding  gear  with 
direct  drive  on  high,  was  used  very  extensively  for  many 
years,  and  is  still  being  used  to  some  extent,  especially  on 
commercial  vehicles. 

As  the  speed  capabilities  of  automobiles  increased  it  be- 
came customary  to  fit  change  gears  giving  iour  forward  gear 
changes  and  one  reverse,  so  as  to  enable  the  operator  to  run 
the  engine  near  its  most  advantageous  speed  under  all  road 
conditions.  Now,  a  four  speed  gear  constructed  on  either  the 
original  Levassor  principle  or  the  direct  drive  principle  comes 
out  exceedingly  long,  as  may  be  seen  from  Fig.  43,  which 
represents  the  non-direct  type.  Not  only  does  this  lead  to  a 
bulky  and  heavy  gear  box,  but  the  shafts,  being  relatively 

r 


FIG.   42. — SLIDING   GEAR   WITH    DIRECT    DRIVE. 

long,  are  likely  to  be  insufficiently  rigid  and  to  spring  and 
bend  under  the  thrust  on  the  gear  teeth,  the  gear  thus  oper- 
ating noisily  and  inefficiently.  The  great  length  with  this 
construction  is  mainly  due  to  the  fact  that  the  gears  on  each 
of  the  shafts  must  be  spaced  relatively  far  apart  so  as  to 
avoid  interference.  This  difficulty  was  first  overcome  by 
Wilhelm  Maybach,  engineer  of  the  Daimler  Motor  Company, 
of  Cannstadt,  Germany,  who  with  a  non-direct  drive  type  of 
sliding  gear  used  two  sliding  sets.  This  principle  was  later  also 
applied  to  the  direct  drive  type,  and  proved  so  popular  that 
at  present  it  is  used  on  pleasure  cars  almost  exclusively,  and 
also  largely  on  commercial  vehicles,  and  not  only  for  four 
speed  gears  but  for  three  speed  as  well. 


72 


SLIDING   CHANGE  SPEED   GEARS. 


Three  speed  and  reverse  gears  usually  have  two  sliding  sets 
and  four  speed  and  reverse  gears  three.  The  several  sliding 
sets  are  operated  by  means  of  a  single  lever,  convenient  to  the 
driver,  which  lever,  in  addition  to  its  motion  for  shifting  the 
gears,  has  a  motion  at  right  angles  to  the  plane  of  the  former 
motion,  for  picking  up  and  dropping  the  different  sliding  sets. 
This  type  of  change  gear  is  known  as  the  selective  type  of 
sliding  gear.  It  has  the  advantage  over  the  other,  the  pro- 
gressive type,  that  the  driver  may  change  directly  from  any 
one  gear  to  any  other  without  passing  through  intermediate 
ears,  which  is  not  possible  with  the  progressive  type  of  gear. 


FIG.  43.— PROGRESSIVE  TYPE  FOUR  SPEED  AND  REVERSE  SLIDING  GEAR. 

A  sketch  of  a  four  speed  selective  sliding  gear  is  shown  in 
Fig.  44.  By  comparing  this  figure  with  Fig.  43  the  saving  in 
length  by  the  use  of  the  selective  principle  becomes  apparent. 
Gear  Material— It  is  absolutely  necessary  to  use  high  grade 
materials  for  the  gears  of  sliding  gear  sets.  Owing  to  the 
fact  that  driving  and  driven  gears  are  often  running  at  greatly 
different  pitch  line  velocities  when  they  are  meshed,  the 
teeth  "clash"  together  with  considerable  force,  and  their  ends 
would  soon  be  battered  up  if  they  were  made  of  soft  metal. 
Hardening  the  gears  involves  considerable  difficulty,  because 
if  they  are  hardened  after  they  are  finished  they  are  very 
likely  to  warp  on  being  quenched,  and  hence  to  run  noisily, 
whereas  if  they  are  hardened  before  being  finished  they  can 
be  finished  only  by  grinding. 


SLIDING  CHANGE  SPEED   GEARS.  73 

The  gears  may  be  made  of  either  ordinary  low  carbon  steel  (so- 
called  case  hardening  steel),  low  carbon  nickel  or  low  carbon 
chrome  vanadium  steel,  all  of  which  steels  are  case  hardened; 
or  they  may  be  made  of  high  carbon  chrome  nickel  or  high 
carbon  chrome  vanadium  steel,  gears  of  these  materials  having 
been  used  both  in  the  natural  state  and  hardened  by  quenching. 
The  last  two  materials  have  exceedingly  high  elastic  limits  when 
properly  heat  treated,  but  they  are  so  difficult  to  forge  and 
machine  that  gears  made  of  them  are  very  expensive.  These 
materials  are  fairly  hard  in  the  natural  state,  and  gears  of 
them  therefore  can  be  used  in  that  state;  but  such  gears  wear 
faster  than  case  hardened  gears,  and  since  they  are  more  ex- 
pensive they  are  now  no  longer  used,  except  possibly  in  ex- 
ceptional cases.  Gears  of  chrome  nickel  and  chrome  vana- 
dium steel  with  a  carbon  content  of  0.45  per  cent.,  hardened 


FIG.  44. — SELECTIVE  TYPE  FOUR  SPEED  AND  REVERSE  SLIDING  GEAR 

through  and  through,  are  used  on  the  higher  grades  of  cars. 
When  gears  are  carbonized  for  case  hardening  the  carbon  is 
allowed  to  penetrate  to  a  depth  of  3*2  inch.  Following  are  the 
standard  specifications  and  heat  treatments  of  steels  suitable 
for  sliding  gears  that  have  been  adopted  by  the  Society  of 
Automobile  Engineers: 

Specification  No.  1020—0.20  per  cent,  carbon  steel.     The  fol- 
lowing composition  is  desired : 

Carbon     0.15%  to  0.25%   (0.20%  desired) 

Manganese     0.30%  to  0.60%   (0.45%  desired) 

Phosphorus     not  over  0.045% 

Sulphur     not  over  0.05% 

This    steel    forges    and    machines    well    and    is    particularly 


74  SLIDING   CHANGE   SPEED    GEARS. 

suited  for  case  hardening.  It  has  an  elastic  limit  of  35,000 
pounds  per  square  inch  in  the  annealed  state  and  as  high  as 
70.000  pounds  when  cold  rolled  or  cold  drawn.  For  sliding 
gears  this  steel  should  be  treated  as  follows:  After  forging, 
machining  and  cutting  the  teeth,  carbonize  at  a  temperature  of 
between  1,600°  and  1,750°  Fahr.,  cool  slowly  in  the  carboniz- 
ing mixture,  reheat  to  1,550-1,625  °  Fahr.,  quench,  reheat  to 
1, 400° -1, 450°,  quench  and  draw  in  hot  oil  at  a  temperature  of 
from  300°  to  450°  Fahr. 

Specification  No.  2320—3^  per  cent,  nickel  steel.  The  fol- 
lowing composition  is  desired: 

Carbon     0.15%  to  0.25%   (0.20%  desired) 

Manganese     0.50%  to  0.80%   (0.65%  desired) 

Phosphorus    not   over   0.04% 

Sulphur    not   over   0.045% 

Nickel     3.25%  to  3.75%   (3.50%  desired) 

The  elastic  limit  of  this  material  in  an  annealed  condition 
is  45,000  pounds  per  square  inch,  with  good  reduction  and 
elongation.  When  suitably  heat  treated  the  elastic  limit  may 
be  brought  up  to  60,000  pounds,  and  even  70.000  pounds  per 
square  inch,  with  better  reduction  of  area  than  in  the  annealed 
state.  This  material  is  carbonized  and  heat  treated  as  fol- 
lows: After  the  gears  are  cut.  carbonize  at  between  1,600° 
and  1,750°  Fahr.,  cool  slowly  in  the  carbonizing  material,  reheat  to 
1,500°-1,550°  Fahr.,  quench  ;  reheat  to  1,300°-1,400°  Fahr.,  quench  ; 
reheat  to  250-500°  Fahr.  and  cool  slowly.  The  last  quenching 
operation  must  be  conducted  at  the  lowest  temperature  at 
which  the  material  will  harden,  which  will  sometimes  be  as 
low  as  1,300°  Fahr. 

Specification  No.  3140. — 0.40  per  cent,  carbon,  chrome  nickel 
steel.  The  following  composition  is  desired: 

Carbon 0.35%  to  0.45%    (0.40%  desired) 

Manganese     0.50%  to  0.80%   (0.65%  desired) 

Phosphorus   not  over   0.04% 

Sulphur    not   over   0.045% 

Nickel     1.00%  to  1.50%   (1.25%  desired) 

Chromium 0.45%  to  0.75%   (0.60%  desired) 

This  steel  contains  a  sufficient  amount  of  carbon  to  harden 
without  being  carbonized.  Heat  treatment  produces  an  elas- 
tic limit  as  high  as  200,000  pounds  per  square  inch,  with  good 
reduction  of  area  and  elongation.  The  steel  is  difficult  to 
forge  and  must  be  kept  at  a  thoroughly  plastic  heat  while 
being  forged,  and  not  hammered  or  worked  after  dropping 
to  ordinary  forging  temperature,  as  cracking  is  liable  to  fol- 


SLIDING  CHANGE  SPEED  GEARS.  75 

low.  Since  the  temperature  range  within  which  forging  is  per- 
missible is  small,  the  steel  must  be  frequently  reheated.  The 
heat  treatment  is  as  follows:  Heat  to  1,500°-1,600°  Fahr., 
quench;  reheat  to  1,450°-1,500°  Fahr.,  quench;  reheat  to  600°- 
1,200°  Fahr.  and  cool  slowly.  This  steel  cannot  be  machined  un- 
less thoroughly  annealed.  The  desired  Brinell  hardness  for 
gears  is  between  430  and  470,  the  corresponding  Shore  hardness 
between  75  and  85. 

Specification  No.  6120. — 0.20  carbon,  chrome-vanadium  steel. 
The  following  composition  is  desired: 

Carbon 0.15%  to  0.25%  (0.20%  desired) 

Manganese     0.50%  to  0.80%  (0.65%  desired) 

Phosphorus     not  over  0.04% 

Sulphur     not  over  0.04% 

Chromium    0.70%  to  1.10%  (0.90%  desired) 

Vanadium     not    less    than  0.12%  (0.18%   desired) 

The  treatment  of  the  above  steel  is  as  follows :  Carbonize  at 
a  temperature  between  1,600°  and  1,750°  Fahr. ;  cool  slowly  in 
the  carbonizing  mixture;  reheat  to  1,65.0°-1,750°  Fahr.,  quench; 
reheat  to  1,475°-1,550°  Fahr.,  quench;  reheat  to  250°-550°,  and 
cool  slowly.  The  heating  for  the  second  quench  should  be  con- 
ducted at  the  lowest  temperature  that  will  harden  the  carbonized 

Specification  No.  6145. — 0.45  per  cent,  carbon  chrome-vanadium 
steel.  The  following  composition  is  desired: 

Carbon     0.40%  to  0.50%  (0.45%  desired) 

Manganese     0.50%  to  0.80%  (0.65%  desired) 

Phosphorus     not  over  0.04% 

Sulphur     not  over  0.04% 

Chromium    0.70%  to  1.10%  (0.90%  desired) 

Vanadium    not   less   than  0.12%  (0.18%  desired) 

This  steel  hardens  without  being  carbonized  and  attains  an 
elastic  limit  of  as  high  as  200,000  Ibs.  per  square  inch.  The 
proper  treatment  for  gears  is  as  follows :  Heat  to  1,525°-1,600° 
Fahr.;  hold  at  this  temperature  one-half  hour  to  insure  thor- 
ough heating;  cool  slowly;  reheat  to  1,650°-1,700°  Fahr., 
quench;  reheat  to  350°-550°  Fahr.,  and  cool  slowly. 

For  the  gear  shafts  0.45  per  cent,  carbon  steel,  3^  .per 
cent,  nickel  (0.30  per  cent,  carbon)  or  0.30  per  cent,  carbon 
chrome  nickel  steel  is  used. 

Gear  Reduction  Ratios — With  very  few  exceptions  sliding 
pinion  change  gears  pfbvide  either  three  or  four  forward 
speeds,  besides  one  reverse  speed.  Four  speed  gear  sets  are 


76  SLIDING  CHANGE  SPEED  GEARS. 

fitted,  as  a  rule,  to  the  more  expensive  pleasure  cars  and  to  the 
larger  sizes  of  commercial  vehicles  manufactured.  It  is  cus- 
tomary to  proportion  the  different  gear  reductions  so  they  will 
substantially  form  a  geometrical  series.  For  instance,  in  a 
three  speed  gear  the  reduction  ratio  of  the  intermediate  gears 
is  generally  about  1.8,  and  that  of  the  low  gears  3.2,  which 
latter  figure  is  substantially  the  square  of  1.8.  If  the  motor  is 
relatively  powerful  in  respect  to  the  weight  of  the  car  and  the 
speed  to  which  it  is  geared  on  direct  drive,  then  these  reduction 
ratios  of  the  gear  set  can  be  made  somewhat  smaller;  in  the 
opposite  case  they  should  preferably  be  somewhat  greater. 

In  four  speed  gears  the  reduction  ratio  of  the  low  gears 
(first  speed  set)  varies  from  3.25  to  4.25,  being  generally  near 
4.  With  a  geometrical  progression,  calling  the  first  speed 

ratio  r,  the  second  speed  ratio  would  be  (ty  \     and  the  third 

speed  ratio  ^  r  t  There  is  a  tendency,  however,  to  make  the 
reductions  of  the  two  intermediate  gears  a  little  smaller,  the 
idea  being  that  the  speed  shall  not  be  too  low  while  driving 
on  the  intermediate  gears,  but  the  first  speed  gear  must  be 
sufficiently  low  to  provide  ample  driving  torque  for  all  emer- 
gencies. The  general  run  of  ratios  falls  within  the  following 
limits : 

First    speed 3.75—4.25 

Second    speed    2      --2.2 

Third    speed     1.4—1.6 

Fourth    speed Direct  drive. 

The  reverse  gear  ratio  is  generally  made  somewhat  greater 
than  that  of  the  low  gear — as  great  as  the  design  permits. 

Arrangement  of  Gears — Referring  to  Figs.  42  and  44,  it  will 
be  seen  that  in  these  gears  (which  represent  the  modern 
types)  the  driving  part  of  the  primary  shaft  carries  a  pinion 
which  meshes  with  a  gear  on  the  secondary  shaft.  These 
two  gears  remain  constantly  in  mesh,  while  the  rest  of  the 
gears  are  shifted  into  mesh  when  it  is  desired  to  use  them. 
It  will  be  noticed  that  the  gear  on  the  secondary  shaft  has 
about  twice  the  pitch  diameter  as  the  driving  pinion  on  the 
primary  shaft,  hence  the  secondary  shaft  runs  at  all  times  at 
about  one-half  the  speed  of  the  engine.  There  is  an  alternate 
construction  in  which  the  constantly  meshed  set  of  gears  is 
located  at  the  rear  end  of  the  gear  box,  but  this  is  subject 


SLIDING  CHANGE  SPEED  GEARS.  77 

to  the  disadvantage  that  when  the  direct  drive  is  in  operation, 
which  it  is  a  very  large  proportion  of  the  time  the  car  is  in 
use,  the  secondary  shaft  runs  at  substantially  twice  engine 
speed,  and  the  pitch  line  velocity  of  the  constantly  meshed 
gears  is  practically  twice  as  great.  This  arrangement  is  now 
nearly  obsolete,  and  with  it  has  passed  the  practice  of  en- 
tirely disconnecting  the  primary  and  secondary  shafts  from 
each  other  when  engaging  the  direct  drive. 

Form  of  Gear  Teeth— There  are  two  forms  of  gear  teeth 
in  use,  the  i4l/2  degree  involute  and  the  stub  tooth.  The  latter, 
which  was  specially  created  to  meet  automobile  requirements,  is 
used  in  the  great  majority  of  cases.  The  involute  tooth,  shown  in 
Fig.  45  at  A,  is  the  standard  form  of  tooth  for  machine  cut  gear- 
ing for  ordinary  purposes.  Its  general  proportions  are  given  in 
the  Appendix  to  Volume  I.  The  tooth  contact  surfaces  make  an 
angle  of  14^  degrees  with  a  radial  plane  through  the  axis  of  the 
gear.  The  stub  tooth,  illustrated  in  Fig.  45  at  B,  is  not  as  high  as 
an  involute  tooth  of  the  same  circular  pitch,  and  has  a  greater 
contact  angle  (20  degrees).  Rules  for  the  general  proportions  of 
stub  teeth  were  also  given  in  the  Appendix  to  Volume  I. 

Stub  tooth  gears 
are  much  stronger 
than  involute  tooth 
gears  of  the  same 
circular  pitch,  and 
that  is  the  reason 
they  have  sup- 
planted the  latter. 
It  is  sometimes 
FIG.  45.— INVOLUTE  14^  DEGREES  TOOTH  urged  against  the 
AND  STUB  TOOTH.  stub  tooth  gear 

that      the      radial 

thrust  between  centres  of  shafts,  which  is  proportional  to  the 
tangent  of  the  pressure  angle,  is  somewhat  greater  with  the  stub 
tooth,  but  since  the  radial  thrust  is  only  a  fraction  of  the  whole 
gear  load  on  the  shafts,  this  objection  is  not  a  very  serious 
one.  Another  special  form  of  tooth,  intended  to  have  some  of 
the  same  advantages  as  the  stub  tooth,  is  known  as  the  "long 
addendum."  While  the  total  working  height  is  tbe  same  as 
that  of  the  standard  involute  tooth,  seven-tenths  of  this  height 
is  above  the  pitch  circle  and  only  three-tenths  below  it  in  the 
pinion ;  three-tenths  above  and  seven-tenths  below  it  in  the  gear. 
Calculation  of  Gears — In  determining  the  necessary  di- 
mensions of  change  speed  gears  it  is  advisable  to  calculate  the 
engine  torque  on  the  basis  of  65  pounds  per  square  inch  brake 
m.  e.  p.,  because  the  permissible  stress  in  the  gear  teeth  decreases 


78  SLIDING  CHANGE  SPEED  GEARS. 

rapidly  as  the  pitch  line  velocity  increases,  hence  the  torque  at 
normal  engine  speed  should  be  figured  with.  The  dimensions  of 
gears  necessary  to  transmit  a  certain  torque  at  a  certain  angular 
velocity  are  calculated  by  means  of  a  formula  given  by  Wilfred 
Lewis  in  a  paper  read  before  the  Engineers'  Club  of  Philadelphia 
in  1893.  This  formula  reads 

w  =  S  p  f  y, 

where  w  is  the  tangential  force  in  pounds;  5",  the  stress  in  the 
material  of  the  teeth,  in  pounds  per  square  inch ;  p,  the  circular 
pitch ;  f,  the  face  of  the  gear  in  inches,  and  y  a  constant  depend- 
ing upon  the  form  and  number  of  teeth  in  the  gear.  The  follow- 
ing table  gives  the  values  of  y  for  14^2  degree  involute  teeth  for 
that  range  of  tooth  numbers  which  is  likely  to  be  used  in  auto- 
mobile work : 

TABLE  I— VALUES  OF  y  FOR  14#  DEGREE  INVOLUTE  TEETH. 

12  teeth 0.067       21  teeth 0.092 

13  "  0.070  23   "  0.094 

14  "  0.072  25 

15  "  0.075  27 

16  "  0.077  30 

17  "  0.080  34 

18  "  0.083  38 

19  "  0.087  43 

20  "  0.090  50 


0.097 
0.100 
0.102 
0.104 
0.107 
0.110 
0.112 

The  above  formula  may  be  rearranged  so  as  to  directly  give 
the  width  of  face  required — 
w 

f  =  (23) 

Spy 

With  stub  tooth  gears,  owing  to  the  fact  that  the  height  of  the 
tooth  is  not  proportional  to  the  circular  pitch,  the  Lewis  formula 
is  not  directly  applicable,  since  the  value  of  the  constant  y 
changes  with  the  pitch  of  the  gear  as  well  as  with  the  number 
of  teeth.  For  this  form  of  gearing  the  following  simplified 
formula  may  be  used: 

w 
f  =  , (24) 

S   2 

where  z  is  a  constant  depending  upon  the  pitch  and  the  number 
of  teeth  in  the  gear.  The  values  of  z  for  the  three  pitches  and 
the  numbers  of  teeth  that  are  likely  to  be  used  in  automobile 
change  geans  are  given  in  the  table  on  the  following  page. 

Pitch  Line  Velocity  and  Allowable  Stress — In  three  speed 
gears  the  pitch  line  velocity  of  the  two  gears  that  remain 
constantly  in  mesh  (where  these  are  located  at  the  motor  end) 
varies  between  90  and  100  per  cent,  of  the  piston  speed ;  in  other 
words,  the  pitch  diameter  of  the  constantly  meshed  pinion  varies 


SLIDING   CHANGE   SPEED   GEARS.  79 

TABLE   II— CONSTANTS    FOR   STUB    TOOTH    GEARS. 


No.  of  Teeth 

5-7  Pitch. 

6-8  Pitch. 

7-9  Pitch. 

14   

0.078 

0.061 

0.051 

'5   

0.081 

0.064 

0.053 

16   

0.083 

0.066 

0.054 

17   

0.084 

0.067 

0.055 

18   

0.086 

0.068 

0.056 

19   

0.088 

0.069 

0.058 

20   

0.090 

0.071 

0.059 

21   

0.091 

0.072 

0.060 

23   

0.093 

0.074 

0.061 

25   

0.095 

0.07S 

0.062 

27   

0.098 

0.077 

0.064 

30   

0.100 

0.079 

0.066 

34   

0.104 

0.082 

0.068 

38   

0.108 

0.085 

0.071 

43   

0.111 

0.088 

0.073 

50   

0.116 

0.091 

0.075 

between  57  and  64  per  cent,  of  the  length  of  piston  stroke,  the 
higher  figure  being  more  suitable  for  high  powered  motors.  In 
four  speed  gears  the  pitch  diameter  of  the  constantly  meshed 
pinion  is  made  from  57  to  77  per  cent,  of  the  length  of  stroke. 
The  average  ratio  between  length  of  stroke  and  pitch  diameter 
of  the  constantly  meshed  pinion  is  0.6  in  three  speed  gears,  and 
0.7  in  four  speed  gears. 

As  to  the  allowable  stress  in  the  material  of  the  teeth,  this 
varies  greatly  with  the  pitch  line  velocity,  and,  of  course,  also 
depends  directly  upon  the  physical  properties  of  the  material 
used.  Besides,  it  is  logical  that  the  stress  in  the  constantly 
meshed  pair  of  gears  should  be  somewhat  less  than  the  stress 
in  the  gears  pertaining  only  to  one  particular  speed,  since  the 
constantly  meshed  pair  works  under  load  as  much  as  the  several 
other  pairs  collectively.  The  author  has  gone  over  the  data  of 
a  great  many  sliding  gear  sets,  and  finds  that  the  following 
stresses  in  gear  teeth  give  good  results  in  the  intermittently 
meshed  pairs  of  gears : 

TABLE  III— ALLOWABLE  UNIT  STRESS  IN  ALLOY  STEEL  GEAR 
TEETH,    CASE   HARDENED. 

Pitch  Line  Velocity.  Allowable  Stress. 

(Ft.  P.  M.)  (Lbs.  P.  Sq.  In.) 

750    30,000 

900    27,000 

1050    24,000 

1200 21,000 

1350    18,000 

1500    .    15,000 


80  SLIDING  CHANGE  SPEED  GEARS. 

TABLE    IV— ALLOWABLE    UNIT    STRESS    IN    CHROME    NICKEL 

AND    CHROME    VANADIUM    STEEL    GEAR    TEETH, 

HARDENED   ALL  THROUGH. 

Pitch  Line  Velocity.  Allowable  Stress. 

(Ft.  P.  M.)  (Lbs.  P.  Sq.  In.) 

750    60,000 

900    53,000 

1050 47,000 

1200    42,000 

1350    38,000 

1500 34,000 

1650    30,000 

1800    27,000 

In  the  above  two  tables  the  pitch  line  velocity  is  based  on  a 
piston  speed  of  1,500  feet  per  minute. 

For  the  constantly  meshed  pair  of  gears  the  stress  in  the  teeth 
should  be  taken  15  per  cent,  less  than  for  the  intermittently 
meshed  gears. 

In  calculating  the  face  of  the  gear  it  is  to  be  remembered 
that  the  engaging  edges  of  the  teeth  have  to  be  chamfered  in 
order  to  insure  positive  meshing,  and  this  chamfering  necessarily 
somewhat  reduces  the  effective  width  of  the  gear  face.  In  pro- 
gressive sliding  gears  some  of  the  gears  are  chamfered  on  both 
sides,  while  in  selective  sliding  gears  the  gears  are  chamfered 
on  one  side  only.  The  loss  in  the  effective  width  of  the  face 
amounts  to  about  &  inch  for  each  chamfer.  Another  thing  that 
deserves  consideration  is  that,  after  the  gear  shifting  linkage  has 
become  somewhat  worn,  there  is  a  possibility  that  when  the  gears 
are  meshed  by  the  operator  they  will  not  be  accurately  opposite 
each  other,  with  the  result  that  some  of  the  face  width  will  be 
ineffective,  and  it  is  well  to  also  allow  iV  inch  for  inaccurate 
meshing  01  the  sliding  gears.  This  makes  a  total  allowance,  for 
chamfer  and  inaccurate  meshing,  of  l/%  inch  for  sliding  gears 
chamfered  on  one  side  only  and  $s  inch  for  sliding  gears  cham- 
fered on  both  sides.  If  it  is  desired  to  make  the  gears  of  carbon 
steel,  case  hardened,  the  stresses  in  the  teeth  must  be  taken 
somewhat  lower  than  the  allowable  stresses  in  alloy  steel  case 
hardened,  for  the  same  pitch  line  velocity. 

Application  of  Formula. — We  will  now  calculate  the  dimen- 
sions of  a  change  speed  gear  for  a  four  cylinder  4x5  inch 
motor,  the  gear  to  be  of  the  three  speed  selective  type.  The 
driving  pinion  would  have  a  pitch  diameter  of 

0.6  x  5  =  3  inches. 
We  will  use  gears  with  6-8  pitch  teeth,  hence  the  pinion  will 


SLIDING   CHANGE   SPEED    GEARS.  .81 

have  18  teeth.  We  found  that  in  three  speed  gears  the  low  speed 
reduction  is  usually  about  3.2,  and  it  is  customary  to  make  the 
reduction  ratio  of  the  constantly  meshed  set  of  gears  the  same 
as  that  of  the  low  gear  set.  Hence  the  reduction  ratio  of  either 
set  should  be  about 


3.2  =  1.8  (approximately), 
and  the  number  of  teeth  for  the  driven  member  of  the  con- 
stantly meshed  set  should  be 

1.8   X    18  =  32    (approximately). 

The  low  gear  set  should  have  the  same  number  of  teeth  as  the 
constantly  meshed  set,  and  the  intermediate  gear  set  should  both 
have  an  equal  number  of  teeth,  since  the  constantly  meshed  set 
gives  the  full  reduction  (1.8)  desired  for  the  intermediate  speed. 
Since  the  sum  of  the  numbers  of  teeth  must  be  the  same  for  each 
set,  each  gear  of  the  intermediate  speed  set  must  have 
18  +  32 
-  =  25  teeth. 

2 

The  torque  of  the  motor,  on  the  basis  of  65  pounds  per  square 
inch  brake  m.  e.  p.  is  (Equation  1)  : 
4X5X4X4X65 
-  —  -  =  108  pounds-feet 

The  pinion  of  the  constantly  meshed  set  has  a  pitch  radius  of  1^4 
inches,  hence  the  tangential  force  on  the  pitch  circle  is 
108   X    12 

=  864  pounds. 


At  1,500  feet  piston  speed  the  pitch  line  velocity  is 
1.5  TT 
-  X   1500  =  1413  ft.  p.  m. 

5 

We  will  assume  that  the  gears  are  to  be  made  from  low  carbon 
alloy  steel  and  to  be  case  hardened,  and  from  Table  III  we  see 
that  at  this  pitch  line  velocity  the  permissible  stress  is 

16,800  pounds  —  15  per  cent.  =  14,300  pounds. 
From  Table  II  we  find  the  value  of  the  constant  z  for  an  18 
tooth  6-8  pitch  gear  to  be  0.068.     Hence,  according  to  equation 
(24),  the  necessary  face  width  is 

864 

-  =  0.888—  say  tt  inch. 
14,300   X    0.068 

The  tangential  force  on  the  pitch  line  of  the  intermediate  gears 
is  greater  than  that  on  the  pitch  line  of  the  constantly  meshed  set 
in  the  proportion  of  the  number  of  teeth  of  those  members  of 
the  constantly  meshed  and  the  intermediate  sets  which  are  se- 
cured to  the  secondary  shaft.  In  the  present  case  the  force  is 


82  SLIDING  CHANGE  SPEED  GEARS. 

32 
864  X  —  =  1,106  pounds. 

25 

The  pitch  line  velocity  of  this  set  at  1,500  feet  piston  speed  per 
minute  is  25 

1,413  X  —  =  1,104  ft.  p.  m. 

•j£ 

At  this  speed  the  allowable  stress  in  the  teeth  (see  Table  III) 
is  23,000  pounds  per  square  inch.  The  value  of  constant  z  for 
25  teeth  of  6-8  pitch  is  0.075.  Hence  the  effective  width  of  the 
face  should  be 

=  0.641  inch, 


23,000  X  0.075 
and  the  total  width  of  face 

0.641  +  0.125  =  0.766  inch  —  say  it  inch. 

For  the  low  gear  set  the  pitch  line  pressure  figures  out  to  1,536 
pounds,  and  the  pitch  line  velocity  to  530  ft.  p.  m.  From  Table 
III  we  hnd  the  allowable  stress  in  the  teeth  to  be  29,000  pounds 
per  square.  inch,  and  the  value  of  constant  z  for  18  teeth  is  0.068. 
Hence  the  total  width  of  face  of  the  low  gear  should  be 

-  -  £§-  -  -  +  o.  125  =  0.905—  soy  \\  inch. 
29,000X0.068 

It  will  be  seen  that  the  widths  of  face  of  the  three  gears  come 
out  almost  the  same,  and,  as  a  matter  of  fact,  in  many  three  speed 
sliding  gears  all  of  the  gears  are  made  of  the  same  face  width. 
Some  designers  simplify  their  calculations  by  merely  calculating 
the  required  width  of  face  for  the  constantly  meshed  set  and 
making  all  other  gears  of  the  same  width  of  face. 

In  practically  every  case  the  sliding  member  of  the  low  gear 
set  serves  also  to  give  the  reverse,  hence  the  face  width  of  the 
reverse  pinions  is  fixed  by  the  face  width  of  the  low  speed  gears 

Pressure  on  Bearings  —  The  earlier  change  gears  of  the  slid- 
ing type  were  fitted  with  plain  bearings,  but  anti-friction 
bearings  present  such  important  advantages  that  they  are 
now  almost  invariably  used  in  this  part  of  a  motor  car, 
radial  ball  bearings  being  used  in  the  majority  of  gear  boxes, 
and  roller  and  cup  and  cone  ball  bearings  in  some  instances. 
The  bearing;  have  considerable  influence  on  the  design  of  the 
case,  and  ;n  order  that  the  proper  sizes  may  be  selected  the 
gear  loads  on  them  have  to  be  accurately  calculated. 

In  Fig.  46  is  shown  a  diagram  of  a  pair  of  gear  teeth  in 
mesh.  We  will  assume  the  teeth  to  be  of  stub  form  and  their 
contacting  surfaces  to  make  an  angle  of  20  degrees  with  the 
plane  through  the  axes  of  the  two  shafts.  The  pressure  be- 


SLIDING  CHANGE  SPEED  GEARS. 


83 


tween  the  two  teeth,  which  is  represented  by  the  line  A  D 
is  normal  to  the  contact  surface.  On  the  other  hand,  the  tan- 
gential load  on  the  gear,  which  is  represented  by  the  line  A  C, 
is  normal  to  the  plane  of  the  axes  and,  therefore,  makes  an  angle 
of  20  degrees  with  the  tooth  pressure  A  D.  In  fact,  the  tooth 
pressure  A  D  may  be  resolved  into  two  components:  one,  A  C, 
normal  to  the  plane  of  the  gear  axes  and  tangential  to  the  pitch 
circles,  which  causes  the  driven  gear  to  turn,  and  the  other,  A  B, 
in  the  plane  of  the  gear  axes,  which  tends  to  force  the  gear  shafts 
apart. 


FIG.  46.—  COMPOSITION  OF  GEAR  TOOTH  REACTION. 
Let  T  be  the  torque  transmitted  by  the  driving  gear  and  r 
its  pitch  radius,  then  the  tangential  force  is 


and  the  tooth  pressure  is 


A  D  = 


TX  12 


r  X  cos  20 

There  is,  however,  another  factor  to  be  taken  into  account, 
namely,  trie  friction  of  the  teeth  as  they  move  over  each  other. 


84  SLIDING  CHANGE  SPEED  GEARS. 

When  the  teeth  first  come  together  their  outer  ends  touch  each 
other,  and  they  partly  slide  and  partly  roll  over  each  other  until 
they  are  in  full  mesh.  This  frictional  force  is  in  the  plane  of 
the  contact  surface  and  is  represented  in  the  diagram  by  A  E. 
The  resultant  of  this  frictional  force  and  the  normal  pressure 
on  the  tooth  surfaces  is  represented  by  A  F.  The  friction  angle 
D  A  F  may  be  taken  at  5  degrees,  which  will  make  the  angle 
between  the  tangential  force  and  the  resultant  of  the  tangential 
force,  the  radial  bearing  pressure  and  the  frictional  force  on  the 
teeth,  25  degrees.  Neglecting  the  fact  that  D  F  is  not  quite  in 
line  with  C  D,  we  may  write 
T  X  12 


A  F  = 


(25) 


r  X  cos  25° 

Equation  (25)  gives  the  resultant  reaction  at  the  tooth  surface 
of  any  pair  of  meshing  gears,  if  T  is  made  equal  to  the  torque 


FIG.  47. 

of  the  driving  member  and  r  equal  to  its  pitch  radius.  It  is 
now  to  be  shown  what  bearing  pressure  results  from  this  tooth 
reaction. 

In  Fig.  47,  A  represents  the  shaft  of  the  driving  pinion  which 
has  a  torque  T  impressed  upon  it  at  some  point  in  front  of  the 
bearing.  This  shaft  is  provided  with  a  lever  arm  B,  representing 
a  portion  of  the  driving  pinion,  which  lever  presses  against  the 
end  of  another  lever  C,  similarly  mounted  upon  the  secondary 
shaft.  The  contact  surfaces  of  the  two  lever  arms  make  an 
angle  of  25  degrees  with  the  plane  of  the  axes  of  rotation,  so 
that  the  pressure  between  them  makes  an  angle  of  25  degrees 
with  a  tangent  to  the  circles  described  by  the  centres  of  the  con- 
tact surfaces.  Now,  the  reaction  of  lever  C  on  lever  B  produces 
a  moment  P  X  r  around  the  axis  of  primary  gear  shaft  A.  The 
principle  that  action  and  reaction  are  equal  and  opposite  applies 


SLIDING  CHANGE  SPEED  GEARS. 


85 


c3 

D 

[ 

LtJ. 

ii- 

R, 

D 

[ 

m 

R2 

to  moments  the  same  as  it  does  to  forces,  and  the  reaction  of 
the  bearing  on  shaft  A  tends  to  turn  lever  B  around  the  centre 
line  of  contact  D,  with  the  same  torque,  but  in  the  opposite 
direction,  as  the  contact  pressure  P  tends  to  turn  the  arm 
around  the  axis  of  p 

shaft^.  Hence  Pi 
represents  the  re- 
action of  the  bear- 
ing on  shaft  A  and 
P2  the  pressure  of 
shaft  A  on  the 
bearing. 

Each  of  the  gears 
i  s  supported  o  n 
two  bearings, 
these  bearings 
being  on  opposite 
sides  of  the  gear  FIG.  48.— DISTRIBUTION  OF  TOOTH  PRESSURE 
respective-  BETWEEN  BEARINGS. 

ly,  and  the  bearing 

pressure  is  distributed  between  them  in  a  certain  proportion 
which  we  shall  investigate  presently.  The  constantly  meshed 
pinion  in  many  gears  is  an  exception  to  this  rule,  since  it  over- 
hangs its  bearing  support.  From  the  above  we  see  that  the 
pressure  on  the  bearings  supporting  any  gear  is  equal  to  the 
resultant  tooth  reaction,  and  in  direction  parallel  to  it.  Another 
thing  to  'be  observed  is  that  the  pressures  on  the  shafts  of  two 
meshing  gears  due  to  the  pressure  between  the  teeth  are  equal 
but  in  opposite  directions.  This  is  easily  seen,  since  the  pressure 
of  the  driving  gear  teeth  against  the  driven  gear  teeth  is  equal 
to  the  reaction  of  the  driven  gear  teeth,  but  in  the  opposite  di- 
rection. 

Next  it  becomes  necessary  to  determine  the  division  of  the 
bearing  pressure  due  to  the  tooth  reaction,  between  the  two 
bearings  supporting  any  gear.  The  shaft  forms  a  beam  sup- 
ported at  both  ends,  with  a  concentrated  load  at  the  centre 
of  the  gear.  Referring  to  Fig.  48,  let  Ri  and  R*  be  the  reac- 
tions at  the  supports,  or  loads  on  the  bearings;  P  the  total 
bearing  load  due  to  one  pair  of  gears;  x,  the  distance  of  the 
centre  of  the  gear  from  the  centre  of  the  left  hand  bearing 
and  y  the  distance  from  the  centre  of  the  right  hand  bearing. 

Then,  taking  moments  around  the  centre  plane  of  the  gear 


g<5 
and 


SLIDING  CHANGE  SPEED  GEARS. 


(P— 


Except   when   the   direct   drive   is   being  used,   two   pairs   of 
gears  are  in  mesh  and  transmitting  power  simultaneously,  viz., 


FIG.  49. — CONSTANTLY  MESHED  AND  INTERMEDIATE  SPEED  GEARS 
(SEEN   FROM   ENGINE   END.) 

the  constantly  meshed  pair  and  one  of  the  other  pairs.  However, 
the  bearing  pressures  due  to  these  two  pairs  of  gears  are  not  in 
the  same  direction,  and  therefore  cannot  be  added  together 
directly,  but  must  be  added  by  means  of  the  parallelogram  of 
forces.  This  may  be  seen  from  Fig.  49,  which  is  a  front  view 
of  the  constantly  meshed  and  intermediate  speed  pairs  of  gears. 
In  this  figure,  Pi  represents  the  reaction  of  the  contsantly 
meshed  gear  C  on  the  constantly  meshed  pinion  A,  and  P2  the 
pressure  of  the  intermediate  pinion  D  on  the  intermediate  speed 
gear  B.  The  loads  on  the  bearings  of  the  primary  shaft  R  are 
equal  and  parallel  to  Pi  and  P2,  while  the  loads  on  the  bearings 


SLIDING  CHANGE  SPEED  GEARS. 


87 


of  the  secondary  shaft  are  equal  and  parallel  to  Pi  and  P2,  but 
oppositely  directed.  All  of  these  forces  make  an  angle  of  25 
degrees  with  the  vertical. 

Therefore,  in  order  to  determine  the  total  load  on  the  different 
bearings  of  the  gear  set  corresponding  to  any  particular  speed  or 
gear,  we  first  calculate  the  bearing  load  due  to  one  pair  of 
gears,  then  find  the  proportion  of  this  on  each  bearing;  next 


FIG.   50. — LAYOUT  OF  GEARSET  UNDER   CALCULATION. 

we  determine  the  bearing  load  due  to  the  other  pair  of  gears, 
then  find  the  proportion  of  this  on  each  bearing  and  finally  add 
the  two  loads  on  each  bearing  together  by  means  of  the  parallelo- 
gram of  forces,  which  can  be  done  either  graphically  or  trigo- 
nometrically. 

We  will  now  carry  this  calculation  through  for  the  gear  set 
whose  gear  dimensions  were  calculated  in  the  foregoing.     This 


88  SLIDING  CHANGE  SPEED  GEARS. 

gear  with  its  bearings  is  laid  out  in  Fig.  50.     The  tangential 
forces  on  the  pitch  circles  we  found  to  be : 

864  pounds  on  the  constantly  meshed   gears; 
1,106  pounds  on  the  intermediate  gears; 
1,536  pounds  on  the  low  speed  gears, 

and  if  we  assume  that  the  reverse  pinion  has   14  teeth,  it  is 
1,975  pounds  on  the  reverse  gears. 
Since  the  bearing  loads  are  equal  to 
Tangential  Force 

cos  25  degrees 

and  the  cosine  of  25  degrees  is  0.906,  we  have  for  the  bearing 
loads  due  to  these  tangential  forces : 

953  pounds  due  to  the  constantly  meshed  gears ; 
1,222  pounds  due  to  the  intermediate  gears; 
1,693  pounds  due  to  the  low  speed  gears; 
2,180  pounds  due  to  the  reverse  gears. 

Now,  assume  the  intermediate  pair  of  gears  to  be  in  operation. 
The  load  on  bearing  I  due  to  the  tooth  pressure  of  the  con- 
stantly meshed  gears  is 

7.469 

953  X  =  832  pounds. 

8.563 
That  on  bearing  II  due  to  this  pressure  is 

953  —  832  =  121  pounds. 

The  load  on  bearing  I  due  to  the  tooth  pressure  of  the  inter- 
mediate gears  is 

4.219 

1,222  X =  602  pounds. 

8.563 
That  on  bearing  II  due  to  this  pressure  is 

1,222  —  602  =  620  pounds. 

Adding  the  two  loads  on  each  bearing  graphically,  as  shown 
in  Fig.  51,  we  find  the  loads  on  bearings  I  and  II  to  be  642  and 
550  pounds,  respectively.  The  directions  of  these  loads  are  as 
indicated  by  the  arrows,  the  gear  being  looked  at  from  the  front. 
The  load  on  bearing  V  due  to  the  tooth  pressure  of  the  inter- 
mediate gears  is 

4.219 

1,222  X  =  708  pounds. 

7.25 

The  load  on  bearing  VI  due  to  the  tooth  pressure  on  the  inter- 
mediate gears  is 

1,222  —  708  =  514  pounds. 

The  load  on  bearing  IV  due  to  the  tooth  pressure  on  the  inter- 
mediate gears  is 


SLIDING  CHANGE  SPEED  GEARS. 


2.969 

708  X  =  1,271  pounds. 

1.656 

The  load  on  bearing  III  due  to  the  tooth  pressure  on  the  inter- 
mediate gears  is 

1,271  —  708  =  563  pounds. 

The  load  on  bearing  III  is  opposite  in  direction  to  the  load  on 
bearing  IV. 


Secondary  Shaft  Bearings 


Primary  Shaft  Bearing* 


FIG.  51. — BEARING  LOADS  FOR  INTERMEDIATE  GEAR  OPERATION 
The  load  on  bearing  IV  due  to  the  tooth  pressure  on  th3  con- 
stantly meshed  gears  is 

953  X  fffiff*  *,&o  pounds. 

The  load  on  bearing  III  due.  to  the  tooth  pressure  on  the  con- 
stantly  meshed  gears  is 

1,580  —  953  =  627  pounds. 


90  SLIDING  CHANGE  SPEED  GEARS. 

The    loads    on   bearings    III    and    IV   while  the    intermediate 
gear  is  in  operation  are  added  together  graphically  in  the  right 


Secondary  Shaft  Bearings      »    Primary    Shaft   Searing 
FIG.  52. — BEARING  LOADS  FOR  Low  GEAR  OPERATION. 

hand  diagram  in  Fig    51,  and  the  magnitude  and  direction  of 
the  load  on  bearing  VI  are  also  shown. 

When  the  low  gears  are  in  mesh  the  bearing  loads  due  to 
the  tooth  pressure  on  the  constantly  meshed  pair  of  gears  will 
be  the  same  as  when  the  intermediate  gears  are  in  mesh,  which 


SLIDING  CHANGE  SPEED  GEARS. 


91 


loads  we  have  already  found.    The  load  on  bearing  I  due  to  the 
tooth  pressure  on  the  low  speed  gears  is 
3.219 

1,693  X  =  637  pounds. 

8.563 

The  load  on  bearing  II  due  to  the  tooth  pressure  on  the  low 
speed  gears  is 

1,693  —  637  =  1,056  pounds. 

Adding  the  two  forces  on  each  bearing  graphically,  as  in  Fig. 
52,  we  find  the  loads  on  the  secondary  shaft  bearings  for  low 


FIG.   53. — MAGNITUDE  AND   DIRECTION   OF   TOOTH   PRESSURE   ON 

REVERSE  GEARS. 

gear  operation  to  be  645  pounds  on  bearing  I  and  981  pounds 
on  bearing  II. 

The  load  on  bearing  V  due  to  the  tooth  pressure  on  the  low 
speed  gears  is 

3.219 

1,693  X  =  753  pounds. 

7.25 

The  load  on  bearing  VI  due  to  the  tooth  pressure  on  the  low 
speed  gears  is 

1,693  —  753  =  940  pounds. 

The  load  on  bearing  IV  due  to  the  tooth  pressure  on  the  low 
speed  gears  is 

2.969 

753  X  =  1,350  pounds. 

1.656 


92  SLIDING  CHANGE  SPEED  GEARS. 

The  load  on  bearing  III  due  to  the  tooth  pressure  on  the  low 
speed  gears  is 

1,350  —  753  =  597  pounds. 

The  loads  on  the  bearings  of  the  primary  shaft  corresponding 
to  low  gear  operation  are  added  graphically  in  the  right  hand 
diagram  in  Fig.  52,  and  we  find  that  the  load  on  IV  is  1,263 
pounds  and  on  III,  513  pounds. 

The  direction  of  the  tooth  pressures  on  the  reverse  gear  and 


Secondary  <5haft  3ectring>s. 


FIG.  54.— BEARING  LOADS  FOR  REVERSE  GEAR  OPERATION. 
pinion  may  be  found  graphically  from  Fig.  53.  It  is  seen  that 
the  pressure  of  the  idler  gear  on  the  reverse  gear  makes  an 
angle  of  10^  degrees  with  the  vertical,  and  the  reaction  of  the 
idler  gear  teeth  on  the  teeth  of  the  reverse  pinion  makes  an 
angle  of  46l/2  degrees  with  the  horizontal. 

The  load  on  bearing  I  due  to  the  tooth  pressure  between  the 
reverse  pinion  and  idler  is 

1094 

2,180  X  -    -  =  278  pounds. 
8.563 


SLIDING  CHANGE  SPEED  GEARS.  93 

The  load  on  bearing  II  due  to  the  tooth  pressure  between  the 
reverse  pinion  and  idler  is 

2,180  —  278  =  1,902  pounds. 

The  load  on  bearing  VI  due  to  the  tooth  pressure  between  the 
reverse  gear  and  idler  is* 

6.156 

2,180  X  =  1,851  pounds. 

7.25 

The  load  on  bearing  V  due  to  the  tooth  pressure  between  the 
reverse  gear  and  idler  is 

2,180  —  1,851  =  329  pounds. 

The  load  on  bearing  IV  due  to  the  tooth  pressure  between  the 
reverse  gear  and  the  idler  is 

2.969 

329  X  =  590  pounds. 

1.656 

The  load  on  bearing  III  due  to  the  tooth  pressure  between  the 
reverse  gear  and  the  idler  is 

590  —  329  =  261  pounds. 

Adding  the  two  loads  on  each  bearing  graphically  (see  Fig. 
54)  we  find  the  loads  on  bearings  I  and  II  to  be  570  pounds 
and  1,789  pounds,  respectively,  and  the  loads  on  bearings  III 
and  IV,  627  pounds  and  2,094,  respectively. 

The  following  table  shows  at  a  glance  the  load  on  each 
bearing  for  each  speed: 

Bearing.  I.  II.          III.          IV.          V.          VI. 

Reverse  570    1789    627    2094    329    1851 

Low  gear  645     981    513    1263    753     940 

Intermediate  gear  642     550    519    1263    708     514 

High  gear  

Bearing  Load  Due  to  Bevel  Gears — Cars  fitted  with  side 
chain  drive  have  a  bevel  gear  set  enclosed  in  the  rear  portion  of 
the  change  gear  box,  the  bevel  pinion  being  keyed  to  the  rear 
end  of  the  primary  shaft.  Of  course,  the  tooth  reaction  of  the 
bevel  gears  throws  considerable  load  on  bearing  VI,  and  this 
must  be  taken  into  account.  In  very  powerful  cars  the  bevel  pin- 
ion is  sometimes  located  between  ball  bearings  on  opposite  sides 
of  it,  but  the  more  common  arrangement  is  to  have  only  a  single 
large  radial  ball  bearing  directly  back  of  the  bevel  pinion.  We 
will  assume  that  in  the  change  gear  under  calculation  the  above 
arrangement  is  used  and  that  the  ratio  of  the  bevel  gear  set  is 
3  to  1.  We  will  further  assume  that  the  pinion  has  eighteen  teeth 
of  6  pitch  and  the  gear  fifty-four.  This  makes  the  maximum 
pitch  diameter  of  the  pinion  3  inches  and  the  pitch  angle  such 


94 


SLIDING  CHANGE  SPEED  GEARS. 


that  its  tangent  is  0.333,  viz.,  18°  26'.     If  the  bevel  pinion  has  a 
face  of  \y%  inches,  then  the  mean  pitch  diameter  is 
3  —  (1^  X  sin  18°  26')  = 
3  —  (!3/£  X  0.316)  =  2.567  inches, 

and  the  mean  pitch  radius,  1.283  inches.  •  Since  the  motor  develops 
a  torque  of  108  pounds-feet,  the  tangential  force  on  the  gear  teeth, 


FIG.  55.— TOOTH  REACTION  IN  BEVEL  GEARS. 

figured  as  though  it  was  concentrated  at  the  middle  of  the  face 
length,  is 

103  X  12 

—  1,010  pounds. 

1.283 

The   tooth   reaction   makes   an   angle   of   20   degrees   with   the 
tangential  force,  hence  its  value  is 

1,010 

=  1,074  pounds. 

0.94 

Now,  in  a  bevel  gear  the  tooth  reaction  is  not  in  a  plane  per- 
pendicular to  the  axis  of  the  gear,  and  for  this  reason  the  bearing 


SLIDING  CHANGE  SPEED  GEARS.  95 

pressure  is  not  equal  to  the  tooth  reaction,  as  in  the  case  of  a 
spur  gear.  We  have  to  resolve  the  tooth  reaction  into  two  com- 
ponents, one  in  a  plane  perpendicular  to  the  gear  axis,  which  is 
equal  and  parallel  to  the  load  of  the  shaft  supporting  bearings, 
and  the  other  in  a  direction  parallel  to  the  gear  axis,  which  is 
equal  to  the  end  thrust.  This  requires  three  successive  steps. 

In  Fig.  55,  A  B  represents  the  normal  pressure  on  the  tooth 
contact  surfaces.  We  first  resolve  this  into  a  component  A  C  in  a 
vertical  plane  perpendicular  to  the  gear  axis,  and  a  component 
C  B  in  a  horizontal  plane  through  the  axis  of  the  gear  and  at 
right  angles  to  the  element  of  the  gear  tooth  surface  on  which 
the  tooth  pressure  comes.  A  D  represents  this  latter  component 
both  in  direction  and  magnitude. 

AD  =  CB  =  AC  tan  20°  =  T  tan  20°. 

The  latter  may  be  resolved  again  into  a  component  A  E  perpen- 
dicular to  the  gear  axis  and  a  component  D  E  parallel  to  the  gear 
axis. 

A  E  =  A  D  cos  B  =  T  tan  20°  cos  6 

D  E  =  A  D  sin  Q  —  T  tan  20°  sin  6  .........................  (26 

D  E  represents  the  end  thrust  of  the  bevel  pinion  which  is 
usually  taken  up  on  the  radial  ball  bearing,  though  some  designers 
provide  a  special  thrust  bearing,  or  use  a  combined  radial  and 
thrust  bearing  at  this  point.  This  equation  is  general  in  its 
nature,  applying  to  all  14^/2  degree  involute  gears;  while  for 
stub  tooth  bevel  gears  tan  25°  should  be  substituted  for  tan  20°. 

The  radial  bearing  load  is  equal  to  the  resultant  of  A  C  and 
A  E  which  is 


an  20°  co  3  0)2  .....................................  (27 

In  our  example  7  =1,010  pounds.  The  tangent  of  20°  is  equal 
to  0.364,  the  cosine  of  0  (18°  25')  is  0.949  and  the  sine  of  0,  0,316. 
Substituting  these  values  in  equations  (26)  and  (27)  we  find  the 
end  thrust  to  be 

1,010X0.364x0.316=116.2  pounds, 
and  the  radial  bearing  load 


vijOio2  +  (1,010  X  0.364  X  o-949)2=  1,051  pounds. 

The  arrow  heads  in  Fig.  55  indicate  the  direction  of  the  reac- 
tion of  the  bevel  gear  teeth  on  the  bevel  pinion  teeth  and  of  its 
components,  and  the  resultant  radial  bearing  pressure  is  in  the 
direction  of  A  F,  which  in  this  case  makes  an  angle  of  22>y2  de- 
grees with  the  vertical. 

Like  the  constantly  meshed  pinion,  the  bevel  pinion  overhangs 
its  bearing.  From  the  centre  of  the  rear  ball  bearing  to  the  centre 


96  SLIDING  CHANGE  SPEED  GEARS. 

cf  the  bevel  pinion  would  be  about  i%  inches,  and  since  the  dis- 
tance between  centres  of  the  two  bearings  of  the  bevel  pinion 
shaft  is  7^4  inches,  we  have  for  the  load  on  bearing  VI  due  to  the 
tooth  reaction  on  the  bevel  pinion : 

M 

1,051  X  ^T=  1,232  pounds, 

and  the  load  on  bearing  V  due  to  the  tooth  reaction  on  the 
bevel  pinion, 

1232  —  1051  =  181  pounds. 

When  the  direct  drive  is  employed  these  are  the  only  loads  on 
bearings  V  and  VI,  but  when  either  of  the  lower  gears  or  the 
reverse  is  in  mesh  the  loads  on  bearings  V  and  VI  due  to  the 
bevel  pinion  tooth  pressure  are  multiplied  by  the  reduction  fac- 
tor of  the  particular  gear,  and  there  is  in  addition  the  load 
due  to  the  reduction  gears  on  bearings  V  and  VI  which  must 
be  combined  with  the  loads  due  to  the  bevel  gears  by  means  of 
the  parallelogram  of  forces.  For  bearing  VI  this  is  done  in 
Fig.  56,  the  values  of  the  loads  on  VI  shown  in  Figs.  51,  52 
and  54  being  used,  and  the  value  of  the  load  due  to  the  bevel 
gears  represented  in  Fig.  55,  multiplied  by  the  reduction  factor 
of  the  particular  gear  combination.  It  will  be  seen  that  the 
bearing  loads  due  to  the  bevel  and  spur  gears  respectively 
partly  neutralize  each  other,  and  that  with  a  gear  of  this  kind 
the  load  on  the  rear  bearing  of  the  primary  shaft  is  greatest 
when  the  low  gear  is  in  operation.  The  tooth  pressure  of  the 
bevel  gears  has  little  influence  on  the  load  on  bearing  V  and  its 
effect  may  be  neglected. 

Sizes  of  Bearings — Manufacturers  of  ball  bearings  issue  tables 
of  load  capacities  with  the  aid  of  which  the  proper  size  of  bearing 
for  each  point  can  be  determined.  These  load  capacities  are  the 
loads  the  bearing  will  stand  under  continuous  running  at  normal 
speed.  Now,  it  will  be  seen  from  the  table  of  bearing  loads  above 
given  that  the  loads  on  all  the  bearings  except  7  and  V  are  a 
maximum  when  the  reverse  gear  is  in  operation,  and  these  maxi- 
mum loads  in  most  instances  are  far  greater  than  the  loads  corre- 
sponding to  the  other  gear  combinations.  It  will  be  remembered 
that  the  bearing  loads  were  calculated  on  the  basis  of  full  engine 
power,  and  it  practically  never  happens  that  the  engine  works  at 
full  load  while  the  reverse  gear  is  being  used.  The  reverse  gear 
is  made  extremely  low  for  the  sake  of  safety  in  backing,  and  not 
because  an  unusually  large  torque  is  needed.  Hence  the  calcu- 
lated bearing  loads  for  the  reverse  gear  never  obtain  in  practice, 
and  they  may  be  neglected  when  selecting  the  proper  size  of  bear- 


SLIDING  CHANGE  SPEED  GEARS. 


97 


FIG.  56. — LOADS  ON  PRIMARY  SHAFT 

REAR  BEARING  (VI)   WHEN 

CARRYING  A  BEVEL  PINION. 


ings,  though  it  is  well  to 
make  sure  that  the  calcu- 
lated load  on  bearing  II 
does  not  exceed  the  rated 
load  by  more  than  100  per 
cent. 

Various  constructional 
and  operative  considera- 
tions often  influence  the 
choice  of  bearing  sizes. 
Thus,  although  there  is  a 
very  considerable  differ- 
ence between  the  maxi- 
mum loads  on  7  and  //, 
these  bearings  are  often 
chosen  of  the  same  size ; 
for  one  reason,  because  it 
simplifies  the  boring  of  the 
bearing  holes  in  the  gear 
case,  since  the  holes  at  op- 
posite ends  can  be  bored 
in  one  operation.  Another 
reason  is  to  be  found  in 
the  advantage  there  is  in 
reducing  the  number  of 
different  parts  in  a  car, 
due  to  the  fact  that  a 
smaller  stock  of  repair 
parts  will  suffice.  When 
it  is  thus  decided  to  use 
the  same  size  of  bearing 
at  both  ends  of  the  sec- 
ondary shaft  the  size  of 
bearing  selected  should 
have  a  rated  load  capacity 
intermediate  between  the 
maximum,  loads  on  the 
two  bearings  for  forward 
running.  Thus  in  our  ex- 
ample the  loads  are  550, 
642,  645  and  981  pounds, 
and  the  No.  306  bearing 
would  probably  be  selected 
which  has  a  rated  capacity 
of  860  pounds.  To  give  a 
general  rule,  the  bearings 
should  be  selected  to  have 


98  SLIDING  CHANGE  SPEED  GEARS. 

a  rated  load  capacity  of  from  75  to  125  per  cent,  of  the  calcu- 
lated maximum  gear  loads  due  to  other  than  the  reverse  gear, 
depending  upon  the  general  quality  of  construction. 

Intermediate  Bearings — In  the  construction  Fig.  50  the 
most  heavily  loaded  bearing  is  IV,  which  is  due  to  the  fact  that 
the  constantly  meshed  pinion  overhangs  this  bearing.  Although 
the  primary  driving  shaft  is  supported  in  two  bearings,  the 
load  due  to  the  tooth  pressure  is  not  divided  between  these  bear- 
ings, as  might  possibly  be  supposed.  The  gear  overhangs  the 
bearings  and  the  load  on  bearing  IV  from  the  constantly  meshed 
gears  alone  is  equal  to  the  tooth  pressure  on  the  constantly 
meshed  pinion  plus  the  load  on  bearing  ///.  The  load  on  bear- 
ing IV  resulting  from  that  on  bearing  V  is  also  nearly  twice  the 
latter.  The  conditions  are  somewhat  more  favorable  when  a 
plain  bearing  is  used  at  V,  extending  a  considerable  distance 
into  the  primary  driving  shaft,  so  that  the  middle  of  its  length 
lies  substantially  in  the  plane  of  bearing  IV,  in  which  case  the 
load  on  V  is  transferred  directly  to  IV.  In  the  case  of  unit 
power  plants  and  designs  of  clutches  requiring  no  slip  joint  in  the 
clutch  shaft,  it  is  advantageous  to  use  only  a  single  bearing  on 
the  primary  driving  shaft,  as  the  load  on  the  bearing  will  then 
be  less  than  that  on  IV  in  Fig.  50. 

In  large  gear  boxes  the  constantly  meshed  pinion  is  some- 
times supported  in  two  bearings,  as  shown  in  Fig.  57,  one  on 
either  side,  the  inside  bearing  being  carried  on  a  pedestal  or  in 
a  partition  wall  in  the  case.  The  loads  are  then  divided  be- 
tween the  two  bearings  in  the  inverse  proportion  of  the  centre 
distances.  Bearing  /  may  also  be  placed  inside  the  constantly 
meshed  gear,  causing  the  latter  to  overhang,  an  arrangement 
that  naturally  suggests  itself  when  the  constantly  meshed  pinion 
is  carried  in  two  bearings.  It  increases  the  load  on  bearing  I 
and  reduces  that  on  bearing  //,  so  their  maximum  loads  will 
be  about  equal,  which  may  be  considered  an  advantage  if  both 
are  to  be  made  of  the  same  size.  However,  this  construction 
is  rare. 

Truck  Change  Gears. — In  change  gears  designed  for  motor 
trucks  the  unit  stresses  are  kept  lower,  for  the  reason  that  trucks 
are  operated  a  great  deal  of  the  time  in  congested  thorough- 
fares where  it  is  necessary  to  do  much  driving  on  the  lower 
gears.  Besides,  a  little  extra  weight  does  not  count  for  so  much 
in  a  truck  as  in  a  high  speed  pleasure  car.  For  this  same  reason 
chrome  nickel  or  other  high  tensile  steels  are  seldom,  if  ever, 
used  for  the  gears  and  pinions  of  truck  transmissions.  With 


SLIDING  CHANGE  SPEED  GEARS.  99 

carbon  steel  and  low  carbon  alloy  steel,  case  hardened,  the  fol- 
lowing unit  stresses  may  be  allowed  in  the  gears  \/    - 

Pitch  Line  Allowable 
Velocity.  Stress. 

(Ft.  p.  m.)  (Lbs.  p.  sq.  in.) 

500     20,000 

600     18,000 

700     16,000 

800     14,000 

900 12,000 

1000     10,000 

The  bearings  of  commercial  change  gears  should  also  be  of 


FIG.  57. — CONSTANTLY  MESHED  PINION  WITH  BEARINGS  ON 
BOTH   SIDES. 

somewhat  more  liberal  size  than  those  in  pleasure  car  gears,  for 
the  same  reason. 

Shaft  Dimensions — One  of  the  chief  requirements  in  a 
change  gear  box  is  quiet  operation,  and  this  necessitates  rigid 
shafts.  The  sizes  of  the  shafts  are,  therefore,  more  dependent 
upon  the  maximum  permissible  flexure  than  upon  the  torque  to 
be  transmitted.  The  tooth  pressure  on  the  gears  located  midway 
between  bearings  creates  an  appreciable  flexure  of  the  shafts, 
and  the  pairs  of  gears  located  near  the  bearings  also  create  some 
flexure,  but  this  may  be  neglected.  The  shafts  should  be  made 
of  such  a  diameter  that  the  maximum  flexure  due  to  any  pair  of 
gears  is  not  more  than  0.003  to  0.005  inch.  In  Chapter  XI  of 
Volume  I  is  given  a  formula  for  the  flexure  of  shafts  supported 


100  SLIDING  CHANGE  SPEED  GEARS. 

at  their  ends  and  carrying  a  concentrated  load  between  hear- 
ings, viz.,    . 


where  P  is  the  load  on  the  shaft  in  pounds  ;  /,  the  length  of  the 
shaft  between  the  centres  of  bearings,  in  inches  ;  d,  the  diameter 
of  the  shaft  in  inches,  and  x  the  ratio  of  the  distance  of  the  load 
from  the  farthest  support  to  the  distance  between  supports. 

Applying  this  equation  to  the  secondary  shaft  of  the  gear  box 
calculated  in  the  foregoing,  in  which  the  flexure  is  evidently  a 
maximum  when  the  low  gear  is  in  operation,  we  have 
P  =  1,693  pounds    I  =  8.563  inches 


2  x*  +  2  x*  —  4  x*  =  0.11 

If  we  decide  to  allow  a  maximum  flexure  of  0.005  inch,  then 
1,693  X  8.563 

X  a11 


8,800,000  X 
and 


.  1,693  X  8.563  X  0.11          ,  „  ,  */.*  •    , 

d  =^    8,800,000X0.005        =  L28  ~  say  1  5/16  wch' 

In  some  designs  of  change  gears  the  secondary  shaft  is  made 
of  somewhat  greater  diameter  in  the  middle  than  at  the  ends, 
•with  the  object  of  securing  the  most  rigid  shaft  with  the  least 
material. 

The  primary  shaft,  since  it  has  substantially  the  same  span 
between  the  supports  and  is  subjected  to  the  same  loads  similarly 
located,  should  be  made  of  practically  the  same  diameter  as  the 
secondary  shaft ;  or,  rather,  it  should  have  a  cross  section  equiva- 
lent to  that  of  the  secondary  shaft  with  respect  to  bending 
stresses. 

Reverse  Gear  Arrangement — Various  arrangements  of  gears 
for  obtaining  the  reverse  motion  are  in  use.  The  most  common 
is  that  already  illustrated  in  Fig.  50,  in  which  the  secondary 
shaft  carries  a  reverse  pinion  sufficiently  smaller  than  the  low 
speed  pinion  to  allow  the  low  speed  gear  to  clear  it  when  shifted 
opposite  it.  This  reverse  pinion  meshes  with  a  reverse  idler  on 
a  special  shaft  mounted  parallel  with  the  primary  and  secondary 
shafts,  usually  in  the  lower  part  of  the  gear  box. 

A  somewhat  different  arrangement  is  shown  in  Fig.  58,  in 
•which  A  is  a  pinion  of  double  width  serving  for  both  the  low 
gear  and  the  reverse;  B  is  the  low  speed  and  reverse  gear  and 


SLIDING  CHANGE  SPEED  GEARS. 


101 


FIG.  58. — REVERSE  GEAR    WITH   Two  IDLERS. 


Ri  R2  are  reversing  idler  gears  on  a  special  short  shaft.  Sliding 
gear  B  is  shown  in  the  position  corresponding  to  the  reverse 
motion.  By  sliding  it  to  the  left  until  it  meshes  with  A  the  low 
forward  speed  is  obtained.  One  advantage  possessed  by  the  ar- 
rangement Fig.  58  over  that  of  Fig.  50  is  that  with  the  former 
there  is  less  strain  on  bearing  II  (at  the  rear  end  of  the  second- 
ary shaft)  than  with  the  latter  when  the  reverse  gear  is  oper- 
ating. 

The  two  types  of  reverse  gear  so  far  shown  are  used  in  three 
speed  selective  and  in  progressive  type  gears.  In  four  speed 
gears  the  reversing  idlers  may  be  arranged  slidably  (see  Fig.  59), 


FIG.  59.— REVERSE  GEAR  WITH   SLIDING  IDLERS. 


102  SLIDING  CHANGE  SPEED  GEARS. 

and  by  means  of  a  separate  sliding  bar  slid  into  mesh  with  both 
the  low  speed  pinion  and  gear  while  the  latter  are  out  of  mesh. 
To  obtain  the  low  speed  forward,  gear  B  is  shifted  to  the  right 
into  mesh  with  pinion  A.  On  the  other  hand,  when  it  is  desired 
to  back  up,  gear  B  is  placed  in  the  neutral  position  (which  it 
occupies  in  the  illustration)  and  reversing  pinions  Ri  and  Rz  are 
slid  to  the  left  into  mesh  with  A  and  B  respectively,  as  shown. 

Direct  Drive  Clutch — There  are  two  types  of  direct  drive 
clutches  in  common  use,  viz.,  the  jaw  type,  illustrated  in  Fig.  60, 
and  the  spur  and  internal  gear  type,  shown  in  Fig.  61.  The 
former  type  consists  of  jaws  formed  on  the  adjacent  faces 
of  the  constantly  meshed  pinion  and  the  intermediate  speed  gear 
respectively.  Usually  each  part  has  four  such  jaws,  equal  in 
size,  and  subtending  at  the  axis  of  the  shaft  an  angle  slightly 
smaller  than  that  subtended  by  the  space  between  them.  The 
outer  edges  of  the  jaws  are  chamfered  to  facilitate  engagement. 
The  radial  width  of  these  jaws  is  usually  made  about  one- 
quarter  the  shaft  diameter  and  the  length  the  same. 

Where  the  spur  and  internal  gear  type  of  clutch  is  employed 
the  constantly  meshed  pinion  often  serves  as  the  spur  member, 
and  the  intermediate  speed  gear  is  cut  with  internal  gear  teeth, 
in  addition  to  its  regular  spur  teeth,  to  serve  as  the  other  mem- 
ber. It  is  somewhat  difficult  to  cut  these  internal  gear  teeth. 
The  job  can  be  done  by  counterboring  the  rim  of  the  spur  gear 
and  then  planing  the  teeth,  but  it  is  a  much  preferable  plan  to 
use  a  form  of  mongrel  teeth  made  by  drilling  holes  into  a  solid 
gear  blank  from  the  side  and  then  chambering  the  blank  out  so 
as  to  cut  away  half  of  the  stock  between  the  holes  (see  Fig.  61). 

Front  Bearing  of  Sliding  Gear  Shaft— Notwithstanding  the 
difficulty  of  keeping  such  a  bearing  effectively  lubricated,  a  plain 
bearing  is  often  used  at  the  forward  end  of  the  squared  or  fluted 
shaft,  on  which  the  gears  slide.  This  construction  renders  non- 
fluid  oil  unsuitable  as  a  gear  box  lubricant.  With  a  fluted  shaft 
the  journal  would  be  made  about  three-quarters  the  diameter  of 
the  shaft  proper  so  as  to  give  a  substantial  shoulder,  and  about 
three  diameters  long.  As  in  the  case  of  the  engine  tailshaft,  large 
oil  holes  and  grooves  are  necessary,  and  the  scheme  of  lubri- 
cation should  be  carefully  worked  out. 

Instead  of  a  plain  bearing,  a  cylindrical  roller  bearing  consist- 
ing of  long,  thin  rollers  is  sometimes  used,  extending  into  the 
counterbore  of  the  shaft,  the  same  as  the  plain  bearing.  How- 
ever, a  more  common  construction  is  to  use  either  a  single  or  a 
double  row  non-adjustable  ball  bearing,  as  illustrated  in  Fig.  61. 


SLIDING  CHANGE  SPEED  GEARS. 


103 


FIG.   60. — DIRECT  DRIVE  JAW  CLUTCH. 

Some  designers  use  a  specially  large  constant  mesh  pinion  in 
order  to  be  able  to  accommodate  a  ball  bearing  of  sufficient 
capacity,  obtaining  the  required  reduction  ratios  by  using  very 
small  intermediate,  low  speed  and  reverse  pinions  on  the  second- 
ary shaft.  The  light  series  of  ball  bearings  is  naturally  best 
adapted  for  this  purpose,  since  it  has  the  least  radial  depth  for  a 
given  load  capacity.  However,  double  row  bearings  seem  to  be 
preferred  for  this  point,  since  it  is  difficult  to  find  room  for  a 
bearing  of  ample  capacity. 

Sliding  Gear  Shaft — As  already  pointed  out,  in  the  earlier 
sliding  change  gears  the  sliding  pinions  were  slid  on  squared 
shafts.  These  are  still  used  to  a  slight  extent,  but  have  for  the 


FIG.  61. — DIRECT  DRIVE  SPUR  AND  INTERNAL  GEAR  CLUTCH. 


104 


SLIDING  CHANGE  SPEED  GEARS. 


most  part  been  replaced  with  splined  or  integral  key  shafts.  The 
two  types  of  shafts  are  shown  in  cross  section  in  Fig.  62.  So- 
called  squared  shafts  are  not  absolutely  square,  but  have  rounded 
corners.  They  are  made  from  round  shafts  by  milling  four  flats 
on  them  to  such  a  depth  that  the  distance  between  opposite  flats 
is  0.8  the  diameter  across  the  corners,  or  the  diameter  of  the 
original  shaft.  Denoting  the  side  of  the  square  formed  by  the 
flats  by  h,  the  torsional  strength  of  such  a  shaft  is  about  0.21  h3S 
pounds-inches,  h  being  given  in  inches.  The  flats  are  often  fin- 
ished by  grinding,  and  if  the  shaft  is  to  carry  long  sleeves  sup- 
porting the  sliding  gears,  they  are  sometimes  cut  with  wavy  oil 
grooves  so  that  oil  may  flow  to  parts  of  the  shaft  that  are  never 
exposed  by  the  sliding  members.  Some  makers  bore  the  hole 
in  the  gear  to  a  slightly  greater  diameter  than  the  side  of  the 


•OJ8<f- 


\ 


FIG.  62. — SECTIONS  OF  SQUARED  AND  SPLINED  SHAFTS. 

squared  shaft,  so  that  when  the  hole  is  broached  out,  from  two- 
thirds  to  three-fourths  of  its  side  will  be  a  plane  surface  and 
the  rest  cylindrical.  (See  Fig.  63.)  This  facilitates  the  broach- 
ing, tends  to  obviate  gripping  of  the  sliding  members  an^  does 
not  appreciably  reduce  the  effective  bearing  surface,  because  the 
pressure  is  localized  near  one  edge  of  the  flat. 

As  compared  with  the  squared  shaft,  the  splined  shaft  pos- 
sesses the  advantage  that  it  takes  the  torsional  load  perpendicu- 
larly on  the  sides  of  the  splines,  whereas  in  a  squared  shaft  most 
of  this  load  comes  close  to  one  edge  of  the  flats,  with  the  result 
that  in  the  latter  the  unit  pressure  may  become  very  high  and 
the  lubricant  may  in  consequence  be  squeezed  out,  which  is  not 
likely  to  occur  with  a  splined  shaft. 


SLIDING  CHANGE  SPEED  GEARS. 


105 


In  American  practice,  splined  gear  shafts  are  made  with  four 
splines  for  small  and  moderate  sized  gear  boxes,  while  in  large 
gear  boxes  six  splines  are  used.  European  practice  tends  to  a 
more  general  use  of  six  splines.  Uneven  numbers  of  splines 
have  also  been  used,  but  they  are  subject  to  the  disadvantage 
that  they  make  it  very  difficult  to  caliper  the  diameters  of  the 
shaft  accurately.  The  ratio  of  the  bottom  diameter  of  a  splined 
shaft  to  the  top  diameter  or  diameter  over  the  splines  is  gen- 
erally about  0.8,  and  the  width  of  the  splines  is  made  about  one- 
quarter  the  bottom  diameter,  or  0.2  times  the  outside  diameter. 
(For  S.  A.  E.  standard  splined  fittings  see  Appendix.) 

Practice  varies  as  to  the  manner  of  locating  the  gears.    Some 


FIG.  63. — BROACHED  SLIDING 
GEAR  WITH  PART  OF 
FLAT  RELIEVED. 


FIG.  64.  —  FLANGE 
BOLTED  GEARS  ON 
SECONDARY 
SHAFT. 


manufacturers  grind  the  outside  of  the  shaft— that  is,  the  top 
surfaces  of  the  keys,  and  let  the  gear  ride  on  these  surfaces, 
using  the  broached  hole  in  the  gear.  Others  grind  out  the  hole 
in  the  gear  (after  the  latter  has  been  hardened)  true  with  the 
pitch  circle  or  the  bottom  circle,  and  let  the  gear  ride  on  the 
bottom  surface  of  the  splined  shaft.  Both  methods  involve  cer- 
tain difficulties,  and  it  is  hard  to  say  which  is  the  better  of  the 
two,  everything  considered. 

Proportions  of  Gears — The  rims  of  gears  below  the  tooth 
annulus  are  made  of  a  thickness  varying  from  0.5  to  0.6  the 
circular  pitch,  and  the  webs  about  the  same.  Since  teeth  of  6  and 
6-8  pitch  are  used  almost  exclusively  in  sliding  gears,  whose  cir- 


106 


SLIDING  CHANGE  SPEED  GEARS. 


cular  pitch  is'  0.52  inch,  both  rim  and  webs  are  generally  made 
Y&,  inch  thick.  When  the  web  is  located  to  come  flush  with  one 
side  of  the  rim,  the  latter  may  taper  from  */i  to  5/16  inch  in 
width,  but  it  is  undoubtedly  preferable  to  have  the  web  central. 
In  this  connection  it  is  worth  remembering  that  substantial  rims 
and  webs  and  liberal  fillets  tend  to  quiet  operation,  and  the 
general  tendency  seems  to  be  toward  a  slight  increase  in  the 
thickness  of  the  sections.  The  smaller  pinions,  of  course,  are 
made  solid,  and  only  the  larger  gears  are  webbed.  As  regards 
the  secondary  shaft  gears,  in  American  practice  they  are  gener- 
ally secured  to  the  shaft  by  means  of  Woodruff  keys,  while 
European  designers,  as  a  rule,  flange-bolt  the  gears  to  the  shaft 


FIG.  65.— SECONDARY  SHAFT  ASSEMBLED  WITH  GEARS  AND 
BEARINGS. 

or  to  a  sleeve  keyed  to  the  shaft.  Frequently  the  gears  for 
the  two  intermediate  speeds  are  bolted  to  the  same  flange,  as 
shown  in  Fig.  64.  One  of  the  reasons  for  flange-bolting  the 
gears  is  that  they  are  then  of  very  simple  form  and  are  not 
so  likely  to  distort  in  hardening.  To  insure  concentricity  the 
web  of  the  gear  is  bored  out  to  fit  accurately  over  an  enlarge- 
ment of  the  shaft.  The  gears  may  also  be  riveted  to  the  flanges. 
The  gears  on  the  secondary  shaft  must  be  accurately  and 
securely  fixed  in  position  longitudinally,  and  this  is  generally 
accomplished  by  turning  the  shaft  with  a  collar  near  its  middle 
against  which  a  gear  is  forced  from  either  end,  and  using  tubu- 
lar spacers  between  these  inner  and  the  outer  gears  on  the  shaft, 
as  shown  in  Fig.  65. 


SLIDING  CHANGE  SPEED  GEARS. 


107 


Instead  of  keying  the  gears  on  the  shaft  and  supporting  the 
latter  in  antifriction  bearings  in  the  housing,  the  entire  set  of 
secondary  gears  may  be  made  in  a  single  forging,  which  re- 
volves on  a  stud  secured  in  the  housing,  as  illustrated  in  Fig. 
66.  Bronze  bearing  bushings  are  forced  into  the  hub  of  the 
gear  set  from  both  ends.  This  construction  is  made  possible 
by  modern  methods  of  gear  planing.  It  is  obvious  that  a  sec- 
ondary gear  set  so  arranged  may  be  made  quite  rigid,  and  as 
the  journal  diameter  is  small,  the  frictional  loss  should  be 
low.  If  the  gear  case  has  a  separate  end  plate  the  shaft  may 


FIG.  66. — SECONDARY  GEAR  ASSEMBLY  ON  STATIONARY  SHAFT. 

even  be  dispensed  with,  the  gear  set  then  being  forged  with 
journals  at  both  ends  which  have  a  bearing  in  the  housing. 

Manufacture  of  Gears — Blanks  for  the  pinions  and  gears 
of  sliding  gear  sets  are  made  either  from  bar  stock  or  from 
drop  forgings,  the  larger  blanks  being  generally  -forged  on 
account  of  the  saving  in  machine  work.  Before  any  work  is 
done  upon  the  blanks  they  should  be  annealed  to  remove  the 
forging  strains,  and  thus  obviate  undue  distortion  during  the 
subsequent  heat  treatment. 

It  is  not  intended  to  go  extensively  into  the  question  of  gear 
cutting  in  this  volume,  because  it  is  an  involved  subject  and  has 


108 


SLIDING  CHANGE  SPEED  GEARS. 


been  ably  treated  in  special  works.  Suffice  it  to  say  that  gear 
teeth  are  either  milled  by  means  of  formed  cutters,  or  planed 
with  ordinary  cutters,  which  by  means  of  templates  or  other 
devices  are  moved  so  as  to  produce  the  proper  shape  of  tooth. 
In  all  gear  cutting  there  are  two  operations,  the  rough  cutting 
or  stocking  and  the  finish  cutting.  Only  very  little  stock  should 
be  left  for  the  latter  operation,  so  that  there  may  be  very  little 


FIG.  67.— FORCING  GEARS  ONTO  SECONDARY  SHAFT. 

strain  on  the  cutting  tool,  and  thus  the  highest  degree  of  ac- 
curacy attained. 

After  the  teeth  are  finish-cut,  the  ends  from-  which  the  gears 
are  to  be  meshed  have  to  be  chamfered.  This  may  be  done  by 
means  of  a  milling  machine  attachment,  as  illustrated  in  Fig. 
68.  The  attachment  is  clamped  to  the  table  of  the  milling  ma- 
chine, and  the  chamfering  tool  is  held  in  the  spindle  of  the  latter. 


SLIDING  CHANGE  SPEED  GEARS. 


109 


The  attachment  comprises  a  work  spindle  on  which  the  gear  to 
be  chamfered  is  mounted,  which  is  alternately  fed  toward  and 
away  from  the  revolving  cutter  by  means  of  a  cam  driven 
through  gearing  from  the  main  shaft  of  the  attachment.  On  a 
secondary  shaft  is  mounted  a  worm  of  the  same  pitch  as  that 
of  the  gear  to  be  chamfered  and  in  which  it  is  meshed.  This 
secondary  shaft  is  driven  through  gears  from  the  main  shaft. 
The  main  shaft  is  driven  by  belt  from  an  overhead  countershaft, 
which  is  entirely  independent  of  the  milling  machine  counter- 
shaft. As  the  main  shaft  revolves  the  worm,  meshing  with  the 


FIG.  68. — "LONG  ARM"  TOOTH  CHAMFERING  ATTACHMENT. 


gear  to  be  chamfered,  turns  it,  and  at  the  proper  intervals  the 
cam  mechanism  feeds  it  toward  and  away  from  the  V-shaped 
revolving  cutter.  The  gear  to  be  chamfered  is  thus  automati- 
cally indexed. 

The  contour  of  the  chamfering  may  be  changed  by  using  spe- 
cial cams,  or  special  cutters,  or  both.  The  profile  at  the  end 
of  the  tooth  may  be  changed  by  swiveling  the  attachment  on  the 


110  SLIDING  CHANGE  SPEED  GEARS. 

table.  The  end  of  the  tooth  may  thus  be  left  at  right  angles 
with  the  axis  of  the  gear  or  at  any  desired  angle. 

The  next  operation  in  the  manufacture  of  the  gears  is  to  harden 
or  case-harden  them.  In  case-hardened  gears,  if  it  is  desired 
that  any  portion  of  the  surfaces  should  remain  soft,  this  can 
easily  be  accomplished  by  leaving  about  1/32  inch  extra  stock  on 
these  surfaces  and  removing  it  after  the  gear  is  carbonized  and 
before  it  is  quenched.  This  practice  also  tends  to  prevent  undue 
distortion  of  the  gear  during  the  quenching.  Another  process 
designed  to  accomplish  the  same  purpose,  and  which  is  undoubt- 
edly less  expensive,  consists  in  copper-plating  the  gears  just 
before  the  finishing  cut  is  taken  and  the  ends  are  chamfered. 
The  result  is  that  when  the  gears  are  carbonized  after  these 
machining  operations  only  those  portions  of  the  gear  from  which 
the  copper  shell  is  removed  will  take  up  carbon  from  the  pack 
and  will  become  hardened  on  being  quenched.  Gears  thus  treated 
are  so  little  distorted  by  the  quenching  that  they  can  readily  be 
corrected  to  the  desired  degree  of  accuracy. 

Every  effort  must  be  made  in  the  manufacture  of  gears  to 
get  every  part  as  nearly  true  as  possible.  It  would  not  seem 
to  matter  much  whether  or  not  the  sides  of  the  gear  blanks  are 
turned  absolutely  true.  This,  however,  is  quite  essential,  for  the 
reason  that  gears  are  generally  cut  in  "gangs,"  a  considerable 
number  of  them  being  forced  over  the  mandrel  and  the  milling 
cutter,  etc.,  then  being  fed  through  the  whole  set  in  one  opera- 
tion. Now,  if  the  sides  of  the  blanks  are  not  absolutely  parallel 
there  is  a  tendency  to  distort  the  mandrel  when  the  nut  is  turned 
up,  and  thus  to  produce  irregularity  in  the  teeth. 

For  the  grinding  of  the  hole  after  the  teeth  are  cut,  as  re- 
ferred to  in  the  foregoing  in  connection  with  splined  shafts,  a 
special  fixture  is  required  for  holding  the  gears.  This  consists 
of  a  face  plate  with  Several  studs  driven  into  it  parallel  with  its 
axis  and  at  such  a  distance  therefrom  that  they  fit  accurately 
between  the  teeth  of  the  gear  at  the  pitch  circle.  These  locate 
the  gear  concentrically  with  the  grinder  spindle,  and  it  may  then 
be  held  in  position  by  means  of  a  couple  of  clamping  plates  and 
bolts.  The  fixture  serves  also  as  a  rough  gauge  for  indicating 
the  accuracy  of  the  gear  cutting  operation.  If  the  teeth  have 
been  cut  too  deep,  the  gear  will  be  loose  in  the  fixture,  whereas 
if  they  have  not  been  cut  deep  enough  it  will  not  enter  between 
the  studs. 

Tester  for  Gears — A  more  delicate  gauge  or  gear  tester 
is  made  as  follows  (Fig.  69)  :  A  vertical  shaft  A  is  fixed  to  a 


SLIDING  CHANGE   SPEED  GEARS. 


Ill 


base  and  provided  with  a  bushing  over  which  fits  the  gear  to  be 
tested.  An  eccentric  stud  B  is  mounted  on  the  base  in  such  a  po- 
sition that  when  the  line  between  its  centres  is  perpendicular  to 
the  line  between  the  axis  of  its  top  portion  and  that  of  the  fixed 
stud,  the  distance  between  the  latter  two  axes  is  the  exact  dis- 
tance between  the  axes  of  the  gear  shafts.  An  indicating  hand 
or  pointer  C  secured  to  the  eccentric  stud  then  points  to  zero. 
The  pointer  moves  over  a  double  scale,  and  therefore  shows 
exactly  how  much  the  gear  is  either  too  small  or  too  large. 

Unless  the  teeth  are  finished  by  grinding  after  hardening — a 
process  that  is  seldom  applied  at  present — some  allowance  must 


FIG.  69. — GEAR  TESTER. 

be  made  for  swelling  or  distortion  during  the  hardening  process, 
by  either  cutting  each  of  the  gears  0.005  to  0.010  inch  small  on 
the  pitch  diameters,  or  else  placing  the  two  shafts  that  much 
farther  apart  than  the  calculated  distance. 

Sliders— The  individual  sliding  members  in  a  gear  set  are 
operated  by  means  of  sliding  bars,  ^  to  ^  mcn  m  diameter,  and 
arranged  parallel  with  the  gear  shafts,  which  carry  forks  that  fit 
into  grooves  formed  in  the  projecting  hubs  of  the  gears.  Two 
such  sliding  bars  are  provided  in  all  three  speed  gears,  and  three 
in  some  four  speed  gears.  Generally  the  sliding  bars  are  placed 


112 


SLIDING  CHANGE  SPEED  GEARS. 


side  by  side,  but  sometimes  they  are  arranged  concentrically. 
The  sliders  are  located  inside  the  gear  box  near  one  of  the  side 
walls  thereof,  and  have  their  bearings  in  the  end  walls.  In  order 
to  insure  accurate  meshing  of  the  gears,  as  well  as  to  lock  them 
out  of  mesh,  a  locking  arrangement  similar  to  that  illustrated 
in  Fig.  70  must  be  provided.  It  consists  of  a  spring  pressed 
plunger  or  ball  which  enters  V  slots  in  the  sliding  bar,  corre- 
sponding to  the  neutral  position  of  the  sliding  set  and  the  two 
or  more  positions  of  engagement,  respectively.  These  locking 
dogs  will  hold  the  slider  in  the  neutral  position  when  it  is  dis- 
connected from  the  operating  lever  and  enable  the  driver  to  find 
the  correct  meshing  position  when  it  is  connected  thereto.  While 
this  method  of  locking  the  sliders  is  not  positive,  it  is  sufficiently 
dependable  for  all  practical  purposes.  In  most  designs  of  selec- 


FIG.   70. — LOCKING   DOG    FOR   GEAR   SLIDER. 

tive  gear  the  operation  of  picking  up  one  slider  with  the  shifting 
lever  entails  the  automatic  and  positive  locking  of  the  other 
sliders. 

Mounting  of  Bearings — If  the  gear  case  is  made  of  aluminum 
and  anti-friction  bearings  are  used,  the  latter  are  generally 
mounted  in  bronze  bushings,  instead  of  directly  in  the  casing. 
This  practice  was  introduced  because  the  aluminum  was  con- 
sidered too  soft,  and  it  was  thought  necessary  to  distribute  the 
pressure  over  a  greater  surface  than  that  of  the  bearings  alone. 
With  the  improvements  which  have  been  made  in  aluminum  al- 
loys in  recent  years  this  is  no  longer  absolutely  necessary,  but 
the  practice  is  still  adhered  to  by  some  designers.  The  bushings 
are  provided  with  outward  radial  flanges  so  as  to  be  held  secure- 
ly against  endwise  motion. 


SLIDING  CHANGE  SPEED  GEARS. 


113 


The  inner  races  of  radial  ball  bearings  should  always  be 
forced  onto  the  shaft  under  moderate  pressure,  and  should  be 
securely  clamped  between  a  substantial  shoulder  on  the  shaft 
and  a  nut  which  is  locked  by  some  approved  means.  Of  the 
outer  races  on  a  single  shaft  not  more  than  one  should  be  firmly 
secured  in  a  lengthwise  direction,  as  otherwise  there  is  danger 
of  subjecting  the  bearings  to  undue  end  thrust. 

Taking  up  the  bearings  on  the  secondary  shaft  first,  the  inner 
races  are  secured  to  the  shaft  as  above  described.  Of  the  outer 
races  one  may  be  clamped  between  an  inward  flange  on  the 
bushing  and  the  bearing  end  cap,  as  shown  in  Fig.  71A,  and  the 
other  one  made  a  sliding  or  "suction"  fit  in  the  casing  or  bush- 


FIG.  71.— MOUNTING  FOR  SECONDARY  SHAFT  BEARINGS. 

ing  and  left  free  to  move  endwise.  An  alternate  arrangement 
consists  in  leaving  both  outer  races  free  endwise  and  taking  up 
the  end  thrust  on  hardened  thrust  buttons  fitted  into  the  shaft 
ends  and  the  bearing  caps,  respectively.  Set  screws  with  rounded 
points  may  be  screwed  through  the  centres  of  the  caps  to  take  the 
place  of  the  buttons  therein  as  shown  at  B  in  Fig.  71. 

The  rule  that  the  inner  races  must  be  firmly  clamped  between 
a  shoulder  and  a  nut  or  spacer  applies  to  all  bearings.  Like- 
wise, if  there  are  two  or  more  bearings  on  one  shaft,  the  outer 
races  of  all  but  one  of  them  should  be  free  endwise,  and  if  a 
thrust  bearing  is  used  in  addition  to  radial  bearings,  the  outer 
races  of  all  the  latter  should  be  free.  In  some  cases  the  for- 


114 


SLIDING  CHANGE  SPEED  GEARS. 


ward  bearing  on  the  primary  shaft  is  subjected  to  the  end  thrust 
of  the  clutch  spring,  and  should  then  be  provided  with  a  ball 
thrust  bearing.  This  is  generally  placed  between  the  two  radial 
bearings.  However,  the  necessity  of  firmly  clamping  both  of  the 
inner  races  on  the  shaft  and  allowing  the  outer  races  some  end- 
wise motion  should  not  be  lost  sight  of  in  this  case.  Fig.  72 
shows  two  ways  in  which  these  requirements  can  be  met.  At  A 
is  shown  the  Alco  design,  which  employs  a  single  thrust  bearing. 
The  design  shown  at  B  is  taken  from  a  paper  read  by  F.  G. 
Barrett  before  the  Institute  of  Automobile  Engineers,  London, 
on  February  14,  1912.  With  the  latter  design  the  thrust  bear- 
ings can  be  properly  adjusted  and  the  adjustments  locked  before 
these  bearings  are  placed  on  the  shaft. 

Geared-up    Fourth   Speed — The   greatest   transmission   effi- 
ciency and  the  most  silent  operation  are  obtained  with  the  direct 


A  B 

FIG.  72.— MOUNTINGS  FOR  PRIMARY  SHAFT  BEARINGS. 


drive,  and  the  designer,  therefore,  should  strive  to  so  propor- 
tion his  gear  reduction  that  the  car  can  be  driven  on  direct 
drive  under  all  normal  conditions.  This  means  that  there  should 
be  a  relatively  large  reduction  between  the  gear  box  and  rear 
wheels.  However,  in  many  types  of  cars  very  high  maximum 
speeds  are  desired,  which  conflicts  with  the  requirement  of  a 
high  reduction  ratio  in  the  final  drive.  These  conflicting  require- 
ments led  to  the  construction  of  four  speed  gears  in  which  the 
direct  drive  is  the  third  speed,  and  the  fourth  is  a  geared-up 
speed,  25  to  30  per  cent,  higher  than  the  direct  drive.  Fig.  73 
shows  the  lay-out  of  the  Winton  change  gear,  with  indirect  fourth 
speed.  The  geared-up  speed  is  obtained  by  placing  on  the  second- 
ary shaft  near  its  rear  end  a  gear  with  a  larger  pitch  diameter 


SLIDING  CHANGE  SPEED  GEARS. 


115 


than  the  constantly  meshed  gear,  adapted  to  be  meshed  with  a 
sliding  pinion  on  the  driven  primary  shaft  of  a  smaller  pitch 
diameter  than  the  constantly  meshed  pinion.  In  a  gear  of  this 
type  it  is  advantageous  to  keep  the  reduction  ratio  of  the  con- 
stantly meshed  pair  of  gears  low,  as  otherwise  the  pitch  line 
velocity  of  the  high  speed  gears  will  be  very  high  and  their 
operation  is  likely  to  be  attended  by  considerable  noise. 

Gear  Cases — The  gear  cases  of  nearly  all  pleasure  cars  are 
cast  of  aluminum  alloy  of  the  same  composition  as  that  used 


FIG.   73. — LAYOUT  OF  WINTON   CHANGE  GEAR  WITH   GEARED- UP 
FOURTH  SPEED. 

for  the  engine  crankcase.  However,  manganese  bronze  is  also 
used  for  that  part  of  the  case  which  supports  the  shafts  and  on 
which  the  greater  part  of  the  strain  comes.  The  gear  boxes  of 
many  motor  trucks,  especially  those  of  European  design,  are 
made  of  cast  steel,  and  cast  iron  cases  are  also  in  use. 
There  are  two  common  arrangements  of  the  shafts  in  a  gear 


116 


SLIDING  CHANGE  SPEED  GEARS. 


box.  Either  the  secondary  shaft  is  located  directly  underneath 
the  primary  shaft  or  the  two  shafts  are  located  in  a  horizontal 
plane.  There  is,  of  course,  a  third  possible  arrangement,  where 
the  plane  of  the  shafts  is  neither  horizontal  nor  vertical,  but  this 
is  seldom  met  with.  Taking  up  first  the  case  of  shafts  in  a  verti- 
cal plane,  the  gear  box  may  be  cast  in  a  single  piece  except  for  a 
large  hand-hole  cover  plate  (Fig.  74)  ;  it  may  be  made  of  a 
shell,  two  end  plates  and  a  hand-hole  cover,  or  it  may  be  divided 
horizontally  through  the  centre  of  the  primary  shaft  bearings. 
Where  the  shafts  are  in  a  horizontal  plane  the  box  may  be  cast 
in  a  single  piece  with  a  large  cover  plate  (Fig.  75),  or  it  may  be 


FIG.  74.— ONE-PIECE  GEAR  CASE  WITH  GEAR  SHAFTS  IN  VERTICAL 

PLANE. 


in  halves  joined  through  the  centres  of  the  bearings  (Fig.  76). 
One-piece  gear  boxes  with  shafts  in  a  vertical  plane  seem  to  be 
preferred  in  connection  with  unit  power  plants,  probably  on 
account  of  the  symmetry  of  outline  obtainable  with  them.  An 
approach  to  symmetry  can  also  be  obtained  with  a  gear  box 
whose  shafts  are  in  a  horizontal  plane,  by  placing  the  shifter 
bars  on  a  level  with  the  gear  shafts  and  allowing  about  the  same 
space  in  the  case  for  these  bars,  the  selecting  lever  and  the  lock- 
ing dogs  as  for  the  secondary  shaft  and  gears. 

The  cases  must  accommodate  not  only  the  gears  and  shafts 
but  also  the  slider  bars,  and  in  most  cases  also  the  selecting 
lever,  though  in  some  instances  this  is  located  outside  the  case. 


SLIDING  CHANGE  SPEED  GEARS. 

JOL 


117 


FIG.   75.— ONE-PIECE  GEAR  CASE  WITH  GEAR  SHAFTS  IN  HORI- 
ZONTAL PLANE. 

Usually  there  is  a  special  lever  house  formed  integral  with  or 
secured  to  the  cover  plate  or  top  half  of  the  case,  in  which  the 
shifter  lever  moves,  the  shaft  of  the  gear  shifting  hand  lever 
passing  through  the  side  walls  of  this  housing. 

The  tendency  among  American  designers  is  to  use  "functional" 
gear  cases;  that  is  cases  with  an  irregular  projection  on  a  plane 
parallel  to  that  of  the  gear  shafts,  whose  walls  at  nearly  every 
point  lie  close  to  some  part  to  be  enclosed.  European  designers, 
on  the  other  hand,  seem  to  be  inclined  toward  box-like  gear 
cases  whose  longitudinal  walls  are  parallel  and  whose  section  is 


FIG.  76.— GEAR  CASE  DIVIDED  THROUGH  AXES  OF  SHAFTS. 


118  SLIDING  CHANGE  SPEED  GEARS. 

such  as  to  cover  with  a  margin  the  end  projection  of  the  entire 
gear.  The  functional  case  is  less  bulky  and  probably  somewhat 
stronger  than  the  box-like  case,  but  the  latter  requires  a  simpler 
pattern  and  is  easier  to  keep  clean. 

Wall  and  Joint  Dimensions — Gear  cases  cast  of  aluminum 
are  made  with  walls  from  3/16  to  %  inch  thick.  At  the  joint  a 
flange  is  run  around  the  outside  on  each  part  which  makes  the 
width  from  y2  to  §^  inch,  the  flange  being  made  *4  to  y%  inch 
high  and  joined  to  the  wall  of  the  case  with  a  liberal  fillet.  The 
halves  are  held  together  by  5/16  inch  bolts  and  nuts  (^  inch  in 
extra  large  gears)  spaced  3  to  4  inches  apart.  Substantial  lugs 
must  be  provided  for  these  bolts,  not  less  than  y2  inch  high. 

Supporting  Methods — Gear  cases  are  supported  on  a  sub- 
frame,  on  cross-members  of  the  main  frame  or  on  the  main 
frame  itself,  the  latter  arrangement  being  rare.  Where  a  sub- 
frame  is  employed  for  carrying  the  engine  and  gear  box,  the 
axis  of  both  usually  lie  from  1  to  \y2  inches  below  the  top  or 
supporting  surface  of  the  frame  members,  whereas  if  the  parts 
are  supported  on  the  main  frame  their  axis  lies  from  4  to  7 
inches  below  the  top  surface  of  the  latter.  The  simplest  method 
of  supporting  the  gear  case  is  that  by  means  of  a  sub-frame,  and 
this  is  generally  used  where  the  shafts  are  in  a  vertical  plane. 
Four  short  arms  are  then  cast  integral  with  the  case,  whose  sup- 
porting surface  is  from  1  to  \l/2  inches  above  the  axis  of  the 
primary  shaft,  and  the  gear  box  is  rested  on  top  of  the  sub- 
frame.  Gear  cases  are  also  often  provided  with  what  is  known 
as  a  three-point  support;  that  is,  the  case  is  cast  with  two  arms 
at  one  end,  resting  either  on  a  sub-frame  or  on  a  cross-member 
of  the  main  frame,  and  at  the  other  end  is  supported  in  a  trun- 
nion carried  on  a  cross-member  of  the  frame  and  surrounding 
the  primary  bearing  hub.  This  gives  a  true  three-point  support. 
An  approximation  to  a  three-point  support  is  obtained  by  using, 
instead  of  the  trunnion,  two  bolts  passing  through  lugs  on  the 
gear  box  on  opposite  sides  of  the  primary  bearing,  and  through 
a  cross-member  of  the  frame. 

When  cross-members  of  the  main  frame  are  used  for  support- 
ing the  gear  box,  the  latter  is  frequently  hung  or  suspended  from 
them,  s*o  that  it  drops  right  out  of  the  car  when  the  supporting 
bolts  are  removed.  Gear  cases  divided  through  the  centres  of 
the  shafts  may  have  the  arms  cast  on  either  half.  The  arms  are 
often  extended  out  from  the  sides  of  the  box  and  are  swung  to 
die  front  and  rear  respectively,  so  that  the  frame  cross-members 


SLIDING  CHANGE  SPEED  GEARS.  119 

will  clear  the  box  proper,  endwise,  thus  making  it  possible  to 
place  these  supporting  members  lower. 

Machining  of  gear  cases  involves  little  difficulty.  If  the  case 
is  made  in  halves  the  first  operation  consists  in  milling  the  faces 
of  the  joint,  of  the  seat  for  the  cover  plate  and  of  the  supporting 
arms.  Next  the  holes  of  the  joint  are  drilled  in  a  multiple 
spindle  drill,  and  finally  the  bearing  holes  are  bored  out  and 
faced  off.  If  the  whole  case  is  cast  in  a  single  piece,  the  machin- 
ing of  the  joint  is  eliminated  and  considerable  work  is  saved. 
Divided  gear  cases  are  used  only  on  the  more  expensive  cars. 

Lubrication  of  Gear  Boxes — Gear  boxes,  as  a  rule,  are  par- 
tially filled  with  non-fluid  oil,  but  those  having  a  parallel  bearing 
on  the  sliding  shaft  generally  require  a  fluid  lubricant.  For  easy 
introduction  of  lubricant  a  hole  is  provided  in  the  cover  plate, 
closed  by  means  of  a  screw  plug,  and  for  washing  out  stale  lubri- 
cant with  kerosene  or  gasoline  a  drain  plug  is  provided  at  the 
lowest  point  in  the  bottom  of  the  case.  Proper  precautions  must 
be  taken  to  prevent  the  oil  or  grease  from  working  out  through 
the  joints  of  the  case  and  around  the  bearings.  The  ends  of  the 
secondary  shaft  bearings  are  closed  by  caps,  and  stuffing  boxes 
or  felt  washers  should  be  placed  on  the  primary  shaft  where 
it  extends  through  the  bearings.  Paper  gaskets  are  placed  be- 
tween the  several  parts  of  the  case. 

It  has  been  found  that  when  the  gears  in  a  gear  box  are 
running  under  load,  the  temperature  within  the  box  is  raised 
considerably  and  the  resulting  air  pressure  tends  to  force  the 
lubricant  out  around  the  protruding  shafts  and  through  joints 
in  the  box.  To  obviate  this,  gear  boxes  are  now  often  provided 
with  breathers  similar  to  those  on  engine  crankcases. 

Running-in  of  Change  Gear — After '  a  change  gear  is  as- 
sembled it  is  run  from  a  line  shaft  for  some  time  in  order  to 
limber  up  its  parts.  While  this  running-in  is  taking  place 
the  case  must  be  well  supplied  with  lubricant.  It  was  formerly 
customary  to  "lap"  the  gears  in  by  running  -them  with  the  case 
partly  filled  with  a  mixture  of  emery  powder  and  oil,  using 
dummy  bearings  for  the  purpose,  but  this  is  no  longer  considered 
necessary. 

The  reverse  idler  is  carried  on  a  plain  bearing.  A  short 
shaft  is  usually  secured  into  a  hub  cast  on  the  wall  of  the  casing 
and  an  integral  support  rising  from  the  base  of  the  latter,  and 
the  idler  is  bushed  with  bronze  and  runs  free  on  this  shaft. 
Large  oil  holes  are  drilled  radially  through  this  gear  and  large 
oil  grooves  are  cut  in  the  shaft. 


120  SLIDING  CHANGE  SPEED  GEARS. 

Efficiency  of  Operation — Comprehensive  tests  of  the  ef- 
ficiency of  a  sliding  pinion  change  gear  were  made  some  years 
ago  by  the  H.  H.  Franklin  Mfg.  Company,  of  Syracuse,  N.  Y., 
and  were  reported  in  THE  HORSELESS  AGE  of  February  12,  1908, 
by  G.  Everett  Quick.  The  gear  tested  was  of  the  three  speed 
and  reverse  progressive  sliding  type.  Its  shafts  were  mounted 
on  radial  ball  bearings  but  the  forward  bearing  of  the  sliding 
shaft  was  hardened  steel  in  bronze.  All  gears  were  cut  with  six 
pitch  teeth  of  %  inch  face  and  were  made  of  ZVz  per  cent,  nickel 
steel,  heat  treated.  The  method  of  making  the  test  was  as 
follows : 

A  direct  current  electric  motor  was  provided  with  a  counter- 
shaft and  a  pulley  thereon  capable  of  serving  as  the  pulley  of  a 
brake  dynamometer.  The  electric  motor  was  then  carefully 
calibrated;  that  is,  tests  were  made  to  accurately  determine  the 
horse  power  output  for  any  input  in  amperes,  the  voltage  re- 
maining constant.  After  a  calibration  curve  had  been  plotted, 
the  electric  motor  was  connected  to  the  driven  end  of  the  change 
gear  and  the  brake  dynamometer  was  transferred  from  the  elec- 
tric motor  to  the  driving  end  of  the  change  gear.  When  a  run 
was  then  made  and  the  electric  motor  consumed  a  certain  num- 
ber of  amperes,  the  power  applied  to  the  change  gear  could  be 
read  off  directly  from  the  calibration  curve  of  the  electric  motor 
and  the  power  delivered  by  the  change  gear  could  simultaneously 
be  determined  by  taking  readings  of  the  dynamometer.  The 
quotient  of  the  power  delivered  by  the  change  gear  to  the  power 
applied  to  it  then  gave  the  efficiency.  The  results  obtained  are 
plotted  in  the  curves  Fig.  77.  It  will  be  seen  that  on  the  direct 
drive  the  efficiency  under  the  most  favorable  conditions  of  speed 
and  output  is  about  98  per  cent.  On  the  intermediate  gear  the 
efficiency  rises  slightly  above  95  per  cent.  On  the  low  gear  it 
attains  94  per  cent,  and  on  the  reverse  about  87  per  cent. 

The  change  gear  used  in  making  the  tests  had  been  run  about 
1,000  miles  in  a  demonstrating  car,  and  the  case  was  about  half 
full  of  heavy  lubricating  oil  during  the  test  A  study  of  the 
curves  will  show  how  a  difference  in  the  pitch  line  velocity  of 
the  gear  and  different  ratios  affect  the  efficiency.  Most  previous 
investigations  of  gearing  efficiency  were  made  at  lower  pitch 
line  velocities.  The  speeds  indicated  in  the  curves  are  those 
at  the  driven  end  of  the  gear. 

Positive  Clutch  Change  Gears — A  design  of  change  gear 
somewhat  related  to  the  sliding  gear  type  is  that  in  which  all  of 


SLIDING  CHANGE  SPEED  GEARS. 


121 


100 
95 

90 
G5 

100 
95 


fi.PJYT. 


Direct 


oJ) 


95 


tf.PJYT. 


X.PJYT. 
500  fi.P.M. 


Speed 


/4 


*       3        4         6        d       /o       J2 
Worse    Power    In  put 

FIG.  77.— EFFICIENCY  CURVES  OF  FRANKLIN  GEAR  Box 


/6        J8 


122 


SLIDING  CHANGE  SPEED  GEARS. 


the  gears  remain  constantly  in  mesh  and  the  gears  on  the  primary 
shaft  are  normally  free  to  turn  thereon  but  may  be  fixed  to  the 
shaft  by  means  of  positive  clutches.  These  clutches,  if  of  the 
jaw  type,  are  proportioned  the  same  as  those  used  for  the  direct 
drive  in  sliding  change  gears.  Difficulties  due  to  meshing  of  the 
teeth  are  avoided  by  the  construction,  but  a  gear  of  this  type  is 
considerably  longer  than  a  sliding  gear  of  the  same  capacity  and 
number  of  gear  changes.  Instead  of  jaw  clutches,  internal  and 
external  gear  clutches  may  be  used.  The  gears  on  the  primary 
shaft  must  be  held  against  endwise  motion  while  the  movable 
clutch  members  must  be  free  to  slide  on  the  primary  shaft  on 
keys  or  squares.  Two  change  gears  of  this  type  are  illustrated 
in  Figs.  78  and  79. 


FIG.   78. — COTTA  POSITIVE  CLUTCH   CHANGE  GEAR. 

Silent  Chain  Change  Gears — The  recent  quest  for  silent 
operation  has  led  to  the  adoption  of  silent  chains  instead  of  spur 
gears  in  change  gear  boxes  by  a  few  European  manufacturers. 
A  notable  example  of  the  use  of  these  chains  is  found  in  the 
gear  boxes  of  London  motor  omnibuses.  Fig.  80  illustrates  this 
change  gear,  which  employs  Coventry  silent  chains.  As  in  the 
case  of  constantly  meshed  gear  sets,  positive  clutches  of  either 
the  jaw  or  internal-external  gear  type  have  to  be  used,  and  this 
combined  with  the  fact  that  for  the  transmission  of  a  certain 
amount  of  power  the  chain  must  be  considerably  wider  than  the 
face  of  a  spur  gear,  makes  the  gear  set  rather  long.  This  ne- 
cessitated the  use  of  a  pair  of  intermediate  bearings  in  the  design 
here  shown.  Naturally,  the  shaft  centre  distance  also  has  to  be 


SLIDING  CHANGE  SPEED  GEARS. 


123 


greater  than  in  a  sliding  gear,  and  this  results  in  a  rather  bulky 
gear  box.  However,  the  London  experience  with  these  gear 
boxes  has  shown  that  not  only  do  they  operate  noiselessly,  but 
the  chains,  notwithstanding  their  short  length,  have  a  very  sat- 
isfactory length  of  life,  even  under  the  very  severe  conditions  of 
omnibus  service  necessitating  frequent  stops  and  acceleration  of 
a  5  ton  load.  One  advantage  claimed  for  the  chain  gear  box 
over  the  spur  type  is  that,  whereas  careless  or  unskilled  operation 
with  the  latter  may  result  in  stripping  of  the  gears,  necessitating 
expensive  repairs,  with  the  former  the  worst  that  may  happen  is 
treakage  of  the  chain,  and  a  new  link  may  easily  be  inserted.  In 


FIG.  79. — Dux  POSITIVE  CLUTCH  CHANGE  GEAR. 

view  of  the  possibility  of  such  breakages  the  gear  box  must  be 
designed  with  enough  room  at  the  bottom  to  contain  the  chain 
without  it  touching  the  chain  wheels,  and  there  must  also  be  a 
liberal  clearance  all  around  the  chain  wheels. 

Some  of  the  points  to  be  observed  in  the  design  of  silent  chain 
change  gears  are  as  follows :  The  distance  between  shaft  centres 
must  be  sufficient  to  allow  of  joining  up  three  or  four  different 
drives  without  excessive  slack  in  any  of  them.  In  the  London 
omnibus  gear  boxes  chains  of  two  different  pitches  (§^j  and  24 
inch)  are  used  in  order  to  solve  the  problem  of  substantially 
equal  centre  distances  without  slack  in  the  chains  for  the  dif- 


124 


SLIDING  CHANGE  SPEED  GEARS. 


ferent  drives.  Pinions  of  less  than  23  teeth  should  preferably 
have  an  odd  number  of  teeth,  in  order  to  insure  the  maximum 
service  from  the  faces  of  the  teeth,  and  the  number  of  links  in 
each  chain  should  be  even.  The  reverse  motion  in  a  silent 
chain  change  speed  gear  is  obtained  in  a  very  simple  manner  by 
means  of  a  pair  of  spur  gears  which  are  slid  into  and  out  of 
mesh. 

In  conclusion  it  may  be  stated  that  silent  chain  gear  boxes 
owe  their  introduction  to  an  order  of  the  London  police  depart- 
ment to  compel  the  London  General  Omnibus  Company  to  re- 
duce the  noise  of  its  omnibuses  (mainly  due  to  worn  gear 
boxes)  or  to  take  them  off  the  streets.  As  yet  these  change 
gears  are  very  little  used  on  stock  cars,  but  in  view  of  the  great 
importance  at  present  attached  to  silent  operation  of  pleasure 


FIG.  80. — SILENT  CHAIN  CHANGE  GEAR. 

cars,  their  more  extensive  introduction  is  within  the  realm  of 
possibility.  In  all  silent  chain  gear  boxes  so  far  built  all  of  the 
chains  run  continuously,  but  it  would  not  be  particularly  dif- 
ficult to  render  all  but  one  of  the  chains  stationary  when  the 
direct  drive  is  in  action. 

In  a  sliding  change  gear  helical  gears  may  be  used  for  the 
constantly  meshed  pair  of  gears  to  reduce  noise.  These  put  ad- 
ditional end  thrust  upon  the  bearings  and  it  is  well  to  keep  the 
angle  of  spiral  moderate,  say  at  20  degrees,  unless  thrust  bear- 
ings are  fitted. 


CHAPTER  IV. 


THE  PLANETARY  CHANGE  GEAR. 

Planetary  or  epicyclic  gear  sets  were  quite  extensively  used  in 
automobile  transmissions  at  one  time,  but  have  lost  much  of  their 
popularity.  They  are  still  being  used,  however,  on  low  priced 
cars  of  both  the  pleasure  and  commercial  types.  This  gear  set  is 
much  cheaper  to  manufacture  than  a  sliding  gear  set,  and  its 
operation  calls  for  less  skill  on  the  part  of  the  driver.  Being 
used  almost  exclusively  on  low  priced  cars,  such  refinements  in 
construction  as  hardened  alloy  steel  gears  and  radial  ball  bear- 
ings are  not  employed  in  planetary  gears.  Generally  these  gears 
are  designed  to  give  only  two  forward  speeds  and  one  reverse. 
It  is  possible  to  obtain  three  forward  speeds  and  one  reverse, 
and  the  Cadillac  Motor  Car  Co.  produced  a  car  with  a  three 
speed  and  reverse  planetary  gear  set  for  several  seasons,  but  the 
addition  of  a  third  speed  introduces  considerable  complication 
and  entails  great  frictional  loss,  and  two  forward  speeds  is  gen- 
erally considered  the  practical  limit  with  this  type  of  gear. 

Principle  of  the  Internal  Gear  Type — There  are  two  gen- 
eral types  of  planetary  gears,  viz.,  those  comprising  internal  gears 
in  their  make-up  and  those  consisting  solely  of  spur  gears,  the 
latter  being  sometimes  referred  to  as  the  "all-spur"  type.  The 
principle  of  the  former  is  illustrated  in  Fig.  81.  A  is  a  driving 
pinion  mounted  either  upon  an  extension  of  the  engine  crank- 
shaft or  upon  a  shaft  connected  to  same,  which  we  will  call  the 
driving  shaft.  This  gear  is  in  mesh  with  two,  three  or  four  equal 
sized  planetary  pinions  B,  evenly  distributed  over  the  circumfer- 
ence of  pinion  A.  Pinions  B  are  supported  upon  short  shafts 
secured  into  the  pinion  carrier  C,  which  may  be  a  disc,  drum  or 
spider  having  a  bearing  upon  the  driving  shaft.  Planetary  pin- 
ions B  B  also  mesh  with  the  internal  gear  D,  which  latter  is 
also  supported  by  having  a  bearing  on  the  driving  shaft.  Two 
such  planetary  sets  as  illustrated  in  Fig.  81  are  required  for  a 
two  speed  forward  and  reverse  gear  set. 

125 


126 


THE  PLANETARY  CHANGE  GEAR. 


The  low  speed  forward  is  obtained  in  the  following  manner : 
Internal  gear  D  can  be  held  from  rotating  by  applying  a  band 
brake  to  its  circumference.  If  pinion  A  is  then  rotated  by  the 
motor  in  a  clockwise  direction,  as  indicated  by  the  arrow,  pinions 
B  will  thereby  be  rotated  around  their  respective  axes  in  a 
counter-clockwise  direction,  and  since  internal  gear  D  is  held  sta- 
tionary by  its  brake,  they  will  roll  on  it  and  carry  pinion  carrier 
C  around  in  a  clockwise  direction ;  that  is,  in  the  same  direction 
as  the  driving  shaft,  but  at  a  lower  speed.  Pinion  carrier  C  is 
in  permanent  driving  connection  with  the  driven  shaft. 

For  the  high  speed  forward  the  driven  shaft  of  the  gear  is 


FIG.  81. — INTERNAL  GEAR  PLANETARY   COMBINATION. 

directly  connected  to  the  driving  shaft  by  means  of  a  friction 
clutch  forming  part  of  the  planetary  gear  set.  Hence,  by  holding 
internal  gear  D  stationary,  motion  will  be  imparted  to  the  driven 
shaft  in  the  same  direction  as  when  it  is  direct  connected  to  the 
engine  shaft  by  the  high  speed  clutch,  but  it  is  revolved  at  a 
lower  speed. 

Calculation  of  Speed  Ratios— Let  a  be  the  number  of  teeth 
in  pinion  A,  and  b  the  number  of  teeth  in  each  of  pinions  B. 
Then  the  number  of  teeth  in  internal  gear  D  is  evidently  a  +  2b. 
We  found  that  the  planetary  pinions,  together  with  the  pinion 


THE  PLANETARY  CHANGE  GEAR.  127 

carrier,  would  rotate  right-handedly  around  the  centre  of  the 
driving  shaft.  Now,  suppose  these  pinions  to  make  one  complete 
revolution  around  the  driving  shaft.  By  rolling  on  the  internal 
gear  D  they  will  be  revolved  around  their  own  axes  the  number 
of  times  their  number  of  teeth  is  contained  in  the  number  of 
teeth  of  internal  gear  D,  viz.  : 


"-+;  ............................................  (18) 

b  b 

However,  this  number  of  revolutions  about  their  own  axes 
represents  only  a  part  of  the  motion  of  planetary  pinions  B;  they 
have  also  at  the  same  time  made  a  complete  revolution  about  the 
axis  of  the  driving  shaft,  and  both  these  motions  must  have  been 
imparted  to  them  by  driving  pinion  A.  By  calculating  the  motion 
of  the  driving  pinion  required  to  produce  each  of  these  motions 
in  the  planetary  pinions,  and  then  adding  the  two  motions,  we 
find  the  number  of  revolutions  of  the  driving  pinion  necessary 
to  produce  one  revolution  of  the  pinion  carrier  C,  and  this,  of 
course,  is  equal  to  the  ratio  of  reduction. 

The  angular  motion  of  the  driving  pinion  to  produce  the  first 
motion  of  the  planetary  pinions  —  that  around  their  own  axes  — 
may  be  found  by  multiplying  the  number  of  revolutions  of  the 

planetaries      /  —  +  2)     by  the  ratio  of  the  number  of  teeth  in 

the  planetaries  to  that  in  the  driving  pinion,  viz.,    —  ,  which  gives 

a 


a  \b          /         a 

To  produce  the  planetary  motion  of  one  complete  revolution 
about  the  driving  shaft  axis  it  is  obvious  that  the  driving  pinion 
must  make  one  revolution  in  the  same  direction  as  that  necessary 
to  produce  the  first  motion  of  the  planetary  pinions.  Hence  the 
total  motion  of  the  driving  pinion  will  be 


(29) 


which  is  the  expression  for  the  low  gear  reduction  with  this  type 
of  planetary  gear. 

Studying  this  expression,  we  see  that  under  no  conditions  can 
the  ratio  of  reduction  be  as  small  as  2.  When  the  planetary  pin- 
ions have  the  same  number  of  teeth  as  the  driving  pinion,  the 
ratio  is  4,  and  when  they  have  half  the  number  of  teeth  (as  in 
Fig.  81),  the  ratio  is  3. 

For  the  reverse  motion  an  arrangement  of  gearing  similar  to 


128  THE  PLANETARY  CHANGE  GEAR. 

that  shown  in  Fig.  81  is  used.  However,  in  this  case  the  pinion 
carrier  C  is  held  from  rotating,  being  provided  with  a  brake  drum 
to  which  a  brake  band  can  be  applied.  If,  then,  the  driving  pinion 
A  is  rotated  in  a  clockwise  direction,  the  planetary  pinions  B 
will  turn  in  a  counter-clockwise  direction  around  their  axes,  and 
the  internal  gear  D  will  be  rotated  by  them  in  a  counter-clock- 
wise direction  around  the  driving  shaft  axis.  In  this  case  internal 
gear  D  is  in  permanent  driving  connection  with  the  driven  shaft 
of  the  gear,  which  latter  is  therefore  rotated  in  the  opposite  direc- 
tion to  the  driving  shaft.  The  ratio  of  reduction  is  merely  the 


FIG.  82.— INTERNAL  GEAR  PLANETARY  COMBINATION  WITH 
DOUBLE  PLANETARY  SETS. 

ratio  between  the  number  of  teeth  in  internal  gear  D  and  driving 
pinion  A;  that  is,  using  the  same  designations  as  in  the  fore- 
going, the  reverse  speed  reduction  ratio  for  this  type  of  plane- 
tary gear  is 

a  +  2b        2b 

=  _  +  1   (30) 

a  a 

In  a  somewhat  modified  design,  illustrated  in  Fig.  82,  the  plan- 
etary pinions  are  made  in  sets  of  two  of  unequal  pitch  diameter 
placed  side  by  side  and  rigidly  connected  to  each  other  or  formed 
integral,  the  smaller  pinion  B  being  in  mesh  with  driving  pinion 


THE  PLANETARY  CHANGE  GEAR.  129 

A,  and  the  larger  one,  B',  with  the  internal  gear  D.  Calling  the 
number  of  teeth  in  the  smaller  planetary  pinion  b  and  the  num- 
ber of  teeth  in  the  larger  one  b',  the  reduction  ratio  for  this  case 
when  internal  gear  D  is  held  stationary  may  be  calculated  as 
follows  : 

The  number  of  teeth  in  the  internal  gear  is  now  a  +  b+b',  and 
the  number  of  revolutions  of  the  planetanes  around  their  axes 
corresponding  to  one  revolution  around  the  driving  shaft  axis 
will  be 

a  +  b  +  b' 

b' 

In  order  to  produce  this  motion  the  driving  pinion  must  make 
b   (a  +  b  +  b'\  __    b      I  \ 

a  (  ----  y  --  )  ~  a^  (  a  +  b  +  b  )  revolutions. 
To  this  must  again  be  added  one  revolution  to  produce  the  plane- 
tary motion  of  the  planetary  pinions,  which  gives  for  the  low 
speed  reduction  ratio  for  this  type  of  gear 


From  this  equation  it  will  be  seen  that  the  reduction  ratio  in- 
creases with  b  and  increases  as  a  and  b'  decrease. 

For  the  reverse  motion  the  pinion  carrier  is  held  stationary 
by  means  of  a  brake  band.  In  this  case,  denoting  the  angular 
velocity  of  internal  gear  D  by  unity,  the  angular  velocity  of  the 
two  planetary  pinions  will  be 

a-\-b  +  b' 

b' 
and  the  angular  velocity  of  the  driving  pinion  is  found  by  mul- 

tiplying this  by  the  factor    —    which  gives 

a 


+          +.,  .......................  (32) 

abf  \  I        b'        abf       a 

When  several  planetary  pinions  are  used  in  an  internal  type 
of  planetary  gear,  the  numbers  of  teeth  in  the  driving  pinion  and 
in  the  planetary  pinions  must  bear  certain  relations  ^to  each  other, 
else  the  gears  cannot  be  assembled.  Let  us  take  the  case  of  a 
planetary  combination  with  three  pinions.  The  number  of  teeth  a 
may  be  divisible  by  3,  a  —  I  may  be  divisible  by  3,  and  a  +  1  may 
be  divisible  by  3.  Hence  there  are  three  different  cases  which 
must  be  investigated  separately.  We  will  assume  that  a  —  i  is 
divisible  by  3.  Then  we  may  write 

a  —  3  x  +  i 
c  —  a  -h  zb 


130 


THE  PLANETARY  CHANGE  GEAR. 


—b  H pitch 


Referring  to  Fig.  83,  if  a  driving  pinion  tooth  centre  coincides 
with  the  line  connecting  the  axes  of  the  driving  pinion  and  the 
top  planetary,  then  a  driving  pinion  tooth  centre  is  at  a  dis- 
tance of  Yz  circular  pitch  from  the  line  connecting  the  driving 
pinion  axis  with  the  axis  of  the  right  hand  planetary  pinioa 


FIG.  83. 

When  the  planetaries  have  an  even  number  of-  teeth,  two  of  their 
tooth  centres  are  opposite.  Hence,  since  a  tooth  centre  on  the 
driving  gear  is  Yz  pitch  ahead  of  the  line  joining  the  driving 
pinion  axis  and  the  right  hand  planetary  axis,  a  tooth  centre  of 
the  internal  gear  will  be  Yz  pitch  beyond  this  line  produced. 
Similarly,  when  the  planetaries  have  an  odd  number  of  teeth,  a 


THE  PLANETARY  CHANGE  GEAR.  131 

space  will  be  directly  opposite  a  tooth,  hence  a  space  centre  of 
the  internal  gear  will  be  on  the  line  connecting  the  axis  of  the 
driving  pinion  to  the  axis  of  the  top  planetary  produced,  and 
another  space  centre  of  the  internal  gear  ^  pitch  beyond  the  line 
connecting  the  axis  of  the  driving  pinion  to  the  axis  of  the  right 

c          1 

hand  planetary  produced.    Therefore,  in  either  case  —  +  —  is  an 

3         3 

c 

integer  which  we  may  denote  by  n.     Substituting  the  value  of  — 

3 
we  have 

2b         1         1 
*  +  —  +  —  +  —  =  «. 

333 
Multiplying  both  sides  by  2 

4b        4 
2x  +  —  +  —  =  2» 

3        3 
But  since  x  and  b  are  integers  we  may  write 

b         4 
_  +  _  =  ni 

3         3 
Multiplying  each  side  by  3,  we  have 

b  +  4  =  3  th. 
Subtracting  3  from  each  side 

b  +  1  =  3  (m  —  1) 

In  other  words,  the  number  of  teeth  in  the  planetaries  must  be 
such  that  when  1  is  added  to  it,  it  is  divisible  by  3. 

The  following  compilation  covers  every  possible  case  with  2,  3 
and  4  planetary  pinions  : 

TWO    PLANETARIES. 

Both  the  driving  pinion  and  the  planetaries  may  have  either  an 
even  or  an  odd  number  of  teeth. 

THREE   PLANETARIES. 

If  a  is  divisible  by  3,  b  must  also  be  divisible  by  3. 

If  a  —  1  is  divisible  by  3,  b  +  1  must  be  divisible  by  3. 

If  a  +  1  is  divisible  by  3,  then  b  —  1  must  be  divisible  by  3. 

FOUR    PLANETARIES. 

If  a  is  even,  b  must  be  even. 

If  a  is  odd,  b  must  be  odd. 

The  object  in  using  more  than  one  set  of  planetary  pinions 
obviously  is  to  divide  the  work  between  these  pinions  and  to  re- 
duce the  strain  on  the  teeth  of  the  other  gears. 

Principle  of  the  All-Spur  Type— One  form  of  the  "all- 
spur"  type  of  planetary  gear  is  illustrated  in  diagram  in  Fig.  84. 


132 


THE  PLANETARY  CHANGE  GEAR 


It  consists  of  three  adjacent,  independent  gears  A  B  D  on 
the  driving  shaft  and  three  corresponding  pinions  A1  B1  D1 
forming  a  single  rigid  planetary  unit.  Gear  A  is  the  driving 
and  gear  D  the  driven  member.  For  the  reverse  motion,  gear 
B,  which  is  mounted  free  on  the  driving  shaft,  is  held  from 
rotation.  Assume  that  the  pinion  carrier  rotates  left  handedly, 
causing  pinion  B1  to  roll  on  B.  For  one  left  hand  revolution 


B* 


FIG.  84.— DIAGRAMS  OF  "ALL  SPUR"  PLANETARY  SET. 


of  the  pinion  carrier,  A*  B1  D1  make  —  left  hand  revolutions 

D1 
around  their  own  axis.     This  results  in  A  making 

6          01 

—  X  —  right  hand  revolutions 

b1          a 

around  its  axis,  which,  combined  with  the  one  left  hand  revo- 
lution due  to  the  motion  of  the  pinion  carrier,  gives  a  total 
motion  of  A  of 


THE  PLANETARY  CHANGE  GEAR.  133 

a1  b 

1  right  hand  revolution 

which  expression  gives  a  positive  value  if  a^ft1.  Similarly, 
the  motion  of  the  planetary  pinions  around  their  own  axis 
causes  D  to  make 

—  X  —  right  hand  revolutions 

ft1  d 

which  combined  with  the  one  left  hand  revolution  due  to  the 
motion  of  the  pinion  carrier  gives 

1  —  left  hand  revolutions 

for  D.    If  this  expression  gives  a  positive  value,  D  will  revolve 
in  the  reverse  direction,  and  this  is  the  case  if  d1<b1. 
The  reduction  ratio  then  is 

a1  ft  a1  ft  —  a  ft1 
1 

a  ft1  a  ft1 

b  d1  ft1  d  ~~~  b  d1 

ft1  a"  ft1  a" 

ft1  d  (a1  6  —  a  b1)         d  (a1  b  —  a  ft1) 

As  the  sum  of  any  pair  of  mating  teeth  must  be  the  same, 
calling  this  sum  x  we  have 

a1   =   x  —   a 

d1   =   x  —   d 

Substituting  in  the  above  equation  for  the  reduction  ratio 
we  have 

d[b  (a?  — a)  —  a  (a?— ft)] 

r  = 

a[d  (x  —  ft)  — ft  (a?  —  a")] 
d  (6  x  —  aft  —  ax  • 


a  (dx  —  db  — 
d  (ft  —  a) 

a  (d  —  b) 

Hence  the  reverse  reduction  ratio  is  dependent  only  on  the 
relative  number  of  teeth  of  the  gears  and  independent  of  the 
planetary  pinions.  It  will  be  seen  at  once  that  this  reduction 
ratio  is  positive  if  ft>a  and 


134 


THE  PLANETARY  CHANGE  GEAR. 


Another  possible  combination  in  which  only  spur  gears  are 
used  is  shown  in  Fig.  85.  A  is  the  driving  gear,  which  meshes 
with  planetary  pinion  B.  An  intermediate  pinion  B1  meshes 
with  both  B  and  the  driven  gear  D.  If  pinion  carrier  C  is  held 
from  rotation,  driven  gear  D  will  revolve  in  the  reverse  direc- 
tion to  that  in  which  driving  gear  A  rotates.  The  variety  of 
gear  arrangements  possible  is  very  large  but  by  means  of  the 
rules  explained  in  the  foregoing  the  direction  of  rotation  and 
gear  ratio  of  any  combination  can  readily  be  determined. 


FIG.   85. — ALL-SPUR    PLANETARY   WITH    DOUBLE   PLANETARY 
PINIONS. 

Assembly  of  Internal  Gear  Type — A  sectional  view  of  an 
internal  gear  type  of  planetary  gear  is  shown  in  Fig.  86.  A  is 
the  driving  shaft,  which  has  secured  to  it  the  low  speed  driving 
pinion  B  and  the  reverse  driving  pinion  C.  Pinion  B  meshes 
with  two  planetary  pinions  D,  which  latter  in  turn  mesh  with  the 
internal  gear  E.  The  rim  of  the  latter  gear  also  serves  as  a 
brake  drum  to  which  a  brake  band  F  may  be  applied,  so  as  to 
hold  the  gear  stationary.  The  planetary  pinions  D  will  then  re- 
volve around  the  axis  of  the  driving  shaft  at  a  low  speed,  as 
already  explained,  and  will  carry  with  them  the  pinion  carrier  G, 
which  latter  is  keyed  to  the  hollow  driven  shaft  H. 

For  the  reverse,  the  brake  band  /  is  applied  to  brake  drum  J, 
which  serves  also  as  a  pinion  carrier  for  the  reverse  planetary 


THE  PLANETARY  CHANGE  GEAR. 


135 


pinions  K.  The  latter  mesh  both  with  the  reverse  driving  pinion 
C  and  the  reverse  internal  gear  L.  Internal  gear  L  and  pinion 
carrier  G  are  rigidly  connected  together,  not  only  by  pinion  pins 
M,  as  shown  in  the  drawing,  but  also  by  bolts  between  the  pin- 
ions. Hence,  when  drum  /  is  held  in  position  by  brake  band  I, 
reverse  pinion  C  will  revolve  internal  gear  L  through  the  inter- 
mediary of  pinions  K  in  the  reverse  (left-handed)  direction,  and 
gear  L  will  communicate  this  reverse  motion  through  the  inter- 
mediary of  pinion  carrier  G  to  driven  shaft  H. 
For  the  direct  drive  the  multiple  disc  clutch  O  is  engaged  by 


FIG.  86. — ASSEMBLY  OF  INTERNAL  GEAR  TYPE  OF  PLANETARY 
GEAR  SET. 

pushing  sliding  cone  Q  to  the  left  under  the  clutch  dogs  S.  One 
set  of  discs  of  the  clutch  is  driven  by  means  of  studs  extending 
from  the  web  of  internal  gear  E,  and  the  other  set  drives  through 
keys  of  the  clutch  hub  P,  which  is  keyed  to  the  driven  shaft  H. 
When  the  clutch  is  engaged  internal  gear  E  and  pinion  carrier  G 
are  locked  together,  hence  planetary  pinions  D  cannot  rotate 
around  their  pins  M,  and  driving  pinion  B  drives  directly  through 
pinions  D,  pinion  carrier  G  and  shaft  H.  The  high  speed  clutch 


^  136  THE  PLANETARY  CHANGE  GEAR. 

can  be  closely  adjusted  by  turning  screw-threaded  collar  R  on 
clutch  hub  P.  When  the  clutch  is  engaged  the  entire  gear  re- 
volves together  as  a  unit,  none  of  its  pinions  working. 

It  is  interesting  to  determine  the  speeds  of  the  different  parts 
while  the  low  gear  is  in  operation.  We  will  assume  that  A  re- 
volves right-handedly  at  1,000  r.p.m.,  that  B  has  24  teeth ;  D,  16 ; 
C,  18,  and  K,  18.  The  low  gear  carrier  and  driven  shaft  will 
then  revolve  (equation  29)  at 
1,000 

Fx"l6  '  r'P'm' 

+  2 

24 
Planetary  pinions  D  will  revolve  on  their  pins  at 

724  \ 

I  —  +  2    1300  =  1,050  r.p.m.  (equation  28) 

\16          / 

One  set  of  clutch  discs  will  be  stationary  and  the  other  set  will 
revolve  at  the  speed  of  the  driven  shaft,  viz.,  300  r.p.m.  In- 
ternal gear  L  will  revolve  right-handedly  at  300  r.p.m.  and 
pinion  C  at  1,000  r.p.m.  Hence  pinion  C  revolves  at  700  r.p.m. 
relative  to  internal  gear  L,  and  drum  /  will  be  revolved  right- 
handedly  at 

.  700 

2X18  ^'^ 

1-2 

18 

Planetary  pinions  K  will  rotate  on  their  pins  at 
3  X  (300  — •  175)  =  375  r.p.m. 
All  of  these  speeds  are  quite  low. 

All- Spur  Planetary  Assembly — Fig.  87  shows  a  longitudinal 
sectional  view  of  an  all-spur  type  of  planetary  gear.  A  is  the 
driving  shaft  which  carries  the  driving  pinion  B,  meshing  with 
planetary  pinions  C.  The  latter  form  part  of  sets  of  three  pin- 
ions, which  are  either  made  integral  or  keyed  together.  D  is  the 
low  speed  planetary  pinion  meshing  with  low  speed  gear  E,  which 
latter  is  secured  to  driven  shaft  F.  By  applying  brake  band  G  to 
the  combined  pinion  carrier  and  brake  drum  H,  the  planetary  pin- 
ions are  held  stationary  in  space  and  act  like  a  back  gear. 
Pinion  B,  rotating  right-handedly,  turns  pinions  C  and  D  on  their 
pin  left-handedly,  and  pinion  D  turns  pinion  E  and  driven  shaft 
F  right-handedly;  that  is,  in  the  same  direction  as  driving  pinion 
B.  For  the  reverse,  brake  band  /  is  applied  to  brake  drum  /, 
-which  has  the  reversing  pinion  K  keyed  to  it.  Gear  K  being  thus 
held  stationary,  when  pinion  B  is  rotated  by  the  engine,  planetary 


THE  PLANETARY  CHANGE  GEAR. 


137 


pinion  L  is  forced  to  roll  on  K  in  planetary  fashion  in  a  left- 
handed  direction,  carrying  the  pinion  pin  M  and  pinion  carrier 
H  with  it. 

The  direct  drive  is  obtained  by  engaging  the  high  speed  clutch 
N,  which  locks  the  reversing  gear  K  to  driving  shaft  A,  and 
since  two  unequal  gears  (B  and  K)  are  now  secured  to  shaft  A, 
the  planetary  pinions  are  locked  against  axial  motion  and  the 
whole  gear  revolves  as  a  unit. 


FIG.  87.— ASSEMBLY  OF  "ALL-SPUR"  TYPE  OF  PLANETARY 
GEAR   SET. 


In  an  "all-spur"  combination,  instead  of  applying  the  power 
through  one  of  the  central  pinions  and  transmitting  it  through  the 
pinion  carrier,  it  may  be  applied  through  the  latter  and  trans- 
mitted through  one  of  the  central  pinions.  The  Ford  change 
gear,  illustrated  in  Fig.  88,  is  of  this  type.  In  this  case  the  fly- 
wheel rim  A  serves  as  the  pinion  carrier  and  driving  member, 


138 


THE  PLANETARY  CHANGE  GEAR. 


having  lateral  studs  secured  into  it  which  carry  triple  planetary 
pinions.  Gear  B  is  the  driven  member,  being  keyed  to  the  hub  of 
clutch  drum  C,  which  in  turn  is  secured  to  driven  shaft  D.  By 
applying  a  brake  band  to  drum  E,  gear  F  is  held  stationary,  pin- 
ion G  rolls  on  it,  and  the  smaller  pinion  H  causes  gear  B  to  turn 
slowly  in  the  same  direction  as  pinion  carrier  A.  By  applying  a 
brake  band  to  drum  /  gear  /  is  held  stationary,  pinion  K  rolls  on 
it,  and  the  larger  pinion  H  turns  gear  B  slowly  in  the  reverse 
direction.  For  the  high  gear  or  the  direct  drive  the  friction  clutch 


, — FORD   PLANETARY  GEAR   SET. 


locks  the  clutch  drum  C  to  the  engine  tailshaft,  and  the  gear 
rotates  as  a  unit. 

Gear  Stresses  and  Bearing  Pressures — The  Pressure  on 
the  pitch  line  of  the  driving  pinion  can  be  calculated  from  the 
engine  dimensions  by  the  method  already  explained.  If  there  are 
several  planetary  pinions  in  mesh  with  the  driving  pinion,  then 
the  total  pressure  on  the  pitch  circle  of  the  driving  pinion  must 
be  divided  by  the  number  of  these  planetary  pinions  in  order  to 
get  the  pressure  on  one  tooth.  The  necessary  width  of  face  of  the 
teeth  can  then  be  calculated  by  the  formula  for  the  strength  of 


THE  PLANETARY  CHANGE  GEAR.  139 

* 

gear  teeth  given  in  the  previous  chapter,  allowing  a  stress  in 
the  teeth  (of  machinery  steel  gears)  at  full  engine  load  of  about 

8,000  pounds  per  square  inch  for  1,400  feet  per  minute 

10,000  pounds  per  square  inch  for  1,200  feet  per  minute 

12,000  pounds  per  square  inch  for   1,000  feet  per  minute 

14,000  pounds  per  square  inch  for      800  feet  per  minute 

pitch  line  velocity  corresponding  to  1,000  feet  per  minute  piston 
speed.  For  nickel  steel  gears  the  stress  in  the  teeth  can  be  made 
20  per  cent,  greater.  In  this  connection  it  should  be  pointed  out 
that  it  is  customary  to  use  ten  pitch  gears  in  planetary  gear  sets 
for  very  small  powers,  say  up  to  15  horse  power,  and  eight  pitch 
gears  for  gear  sets  of  from  15  to  30  horse  power.  In  the  few 
instances  where  planetary  gears  have  been  used  for  larger  powers 
six  pitch  teeth  have  been  used. 

Now,  let  it  be  required  to  calculate  the  dimensions  of  a 
planetary  gear  for  a  double  cylinder  engine  of  4^  inch  bore  by 
4  inch  stroke.  The  calculations  are  somewhat  different  for  the 
internal  type  of  planetary  gear  and  the  all-spur  type,  and  we  will 
carry  the  calculation  through,  first  for  the  one  and  then  for  the 
other.  As  far  as  the  strength  of  gears  and  the  bearing  surface 
required  for  the  planetaries  are  concerned,  the  stresses  and 
pressures  during  low  gear  operation,  of  course,  are  much  more 
important  than  the  stresses  and  pressures  corresponding  to  the 
reverse  motion,  for  the  reason  that  the  reverse  is  never  used  con- 
tinuously for  any  length  of  time.  Suppose  that  a  gear  reduction 
of  3  is  desired  for  the  low  speed  forward. 

The  normal-speed  torque  of  our  motor  is 
2  X  4  X  4^2  X  65 

=  55  pounds-feet. 

192 

We  will  first  carry  the  calculation  through  for  the  internal  type 
of  planetary  gear.  In  order  that  we  may  get  the  desired  reduc- 
tion ratio  the  driving  pinion  and  planetary  pinions  must  be  made 
with  such  numbers  of  teeth,  a  and  b,  respectively,  that 

2JL 

hence 


The  smallest  practical  number  of  teeth  in  a  pinion  is  12,  and  it 
is  well  to  use  a  few  more.  We  will  make  b  =  14  and  a  =  28. 
Also,  we  will  use  8  pitch  standard  14J4  degree  involute  teeth. 
Hence  the  pitch  diameter  of  the  driving  pinion  is  Z1A  inches  and 


140  THE  PLANETARY  CHANGE  GEAR. 

> 

the  pitch  radius  1^4  inches.  Since  the  torque  that  must  be  trans- 
mitted by  this  pinion  is  55  pounds-feet,  the  pitch  line  pressure  is 

55  X  12 

-  =  377  pounds. 

134 

We  will  assume  that  two  oppositely  located  planetary  pinions 
are  used,  so  this  pressure  is  exerted  by  two  teeth  of  the  driving 
pinion,  and  the  pressure  of  each  tooth  is 

377  ==I88.  5  pounds. 

2 

At  1,000  feet  piston  speed  per  minute  the  4  inch  stroke  motor 
turns  at 

1,000  X  12 

2X4        =I'5°°  r.t-™-> 
and  the  pitch  line  velocity  of  the  driving  pinion  is 

1,500X3-5X3-14 
~~ 


Hence  we  may  figure  on  a  stress  of  8,000  pounds  per  square  inch 
in  the  teeth.    Then,  according  to  Lewis'  equation, 

188.5  =  8,000X0.4X^X0.072, 
and 

/=  -  J^5  --  =  0.81  -  say,  1L  inch. 
8,000  X  0.4  Xo.oy2  16 

The  tangential  force  P  on  one  of  the  planetary  pinions  we 
found  to  be  188.5  pounds.  As  indicated  in  Fig.  89,  this  force  is 
exerted  by  the  driving  pinion  on  the  planetary  pinion,  and  there 
is  an  equal  reaction  of  the  internal  gear  on  the  opposite  side  of 
the  planetary  pinion.  Hence  the  pressure  on  the  bearing  of  the 
planetary  pinion  is 

188.5  4-  188.5  =  377  pounds. 

In  a  gear  of  the  internal  planetary  type  it  is  difficult  to  provide 
large  enough  bearing  surfaces,  and  the  unit  pressure  on  the  pinion 
pins  is  usually  in  the  neighborhood  of  600  pounds  per  square 
inch.  This  unit  pressure  in  our  case  calls  for  a  bearing  surface  of 

377       -, 

g^  =  Y&  square  inch. 

If  we  make  our  pin  $/&  inch  in  diameter  it  must  have  a  length 
of  I  inch,  or  slightly  more  than  the  face  of  the  gear. 

It  is  customary  to  make  the  pinions  of  the  reverse  combination 
of  the  same  width  of  face  as  the  pinions  of  the  low  gear  combina- 
tion. 

A  reduction  of  3  to  I  is  practically  the  lowest  obtainable  with 


THE  PLANETARY  CHANGE  GEAR 


141 


this  type  of  gear,  because  for  lower  reductions  the  planetary 
pinions  become  very  small  and  their  rotative  speeds  excessively 
high.  On  the  other  hand,  with  only  two  speeds  forward  the  low 
speed  ratio  is  generally  wanted  comparatively  small,  between 
2  anci  3,  so  that  the  step  from  high  to  low  speed  may  not  be 
too  great. 

Calculation  of  "All  Spur"  Type— With  the  usual  "all  spur" 
type  we  obtain  our  low  forward  speed  by  means  of  a  back 
gear.  The  low  gear  ratio  should  be  approximately  3:1.  If 
two  sets  of  planetary  pinions  are  to  be  used  then  each  of  the 
central  gears  must  have  an  even  number  of  teeth.  Gear  com- 
binations which  give  the  required  reduction  ratios  can  be 


FIG.     89. — TANGENTIAL     AND 

BEARING  PRESSURES  IN 

INTERNAL  GEAR  TYPE 

OF  PLANETARY. 


FIG.  90.— TOOTH  PRESSURES  IN 

ALL-SPUR  TYPE  OF 

PLANETARY. 


found  only  by  trial.  In  selecting  combinations  it  must  be  re- 
membered that  d  must  be  greater  than  &  and  &  greater  than  a 
and  that  the  sums  of  the  teeth  of  all  mating  pairs  must  be 
alike.  A  suitable  combination  is  as  follows: 

a    =  16  &    =  28  d   =  32 


a1  =  28 


&1  =  16 


d1  =  12 


Since  the  low  gear  ratio  is  equal  to  a1  &/  a  b1  we  get  for  it 

28  X  28 

=  3.06 

16  X   16 


142  THE  PLANETARY  CHANGE  GEAR. 

The  expression  for  the  reverse  ratio  is 
d  (b  —  a) 


a(d  —  b) 
hence  its  value  is 

32  (28  —  16) 

=  6 


16   (32  —  28) 

This  reverse  ratio  is  somewhat  greater  than  usually  em- 
ployed, but  a  great  reduction  seems  to  be  desirable  as  it  in- 
sures safety  in  backing.    With  the  usual  sliding  gear  transmis- 
sion the  reverse  gear  ratio  is  always  made  as  great  as  possible. 
The  pitch  radius  of  the  16  tooth  8  pitch  driving  pinion  is  1  inch, 
hence  the  pitch  line  pressure  is 
55  X  12 
=  660  pounds. 

Of  this  one-half,  or  330  pounds,  comes  on  one  tooth.    The  pitch 
line  velocity  is 

1,500  X  2  X  3.14 

=  785  ft. p.m., 

12 

hence  we  may  allow  a  tooth  stress  of  14,000  pounds  per  square 
inch.    Inserting  in  the  Lewis  formula  we  have 

330  =  14,000  X  0.4  X  /  X  0.077 
and 

330 

/  = =  0.755,  say  ft  inch. 

14,000  X  0.4  X  0.077 

In  this  case  the  low  speed  motion  is  not  transmitted  through  the 
gear  carrier,  and  the  whole  force  of  the  drive  does  not  come  on 
the  pinion  pin.  In  Fig.  89  are  shown  the  pressure  of  the  driving 
pinion  tooth  on  the  planetary  pinion  tooth  and  the  reaction  of  the 
stationary  gear  tooth  on  the  tooth  of  the  second  planetary  pinion. 
The  tangential  pressure  on  the  driving  gear  we  found  to  be 
660  pounds.  The  tooth  reaction  between  the  driving  pinion  and 
the  first  planetary  is 

330 

=  350  pounds. 

cos  20° 

The  tooth  reaction  between  the  second  planetary  pinion  and  the 
stationary  pinion  is 

28 

—  X  350  =  612  pounds. 

16 

These  two  pressures  make  an  angle  of   140  degrees  with  each 
other,  and  their  resultant  is  found  graphically  to  be  410  pounds. 


THE  PLANETARY  CHANGE  GEAR.  143 

In  gears  of  this  type  the  unit  pressure  can  be  made  about  200 
pounds  per  square  inch,  hence  we  require 
410 

=  2.05  square  inches 

200 

bearing  surface.  Allowing  a  distance  of  %  inch  between  pinions, 
the  total  length  of  the  pin  bearing  will  be  2%  inches,  and  the 
diameter  of  the  pin  should  be 

2.05  13 

=  0.82.  say,  —  inch. 

2.5  16 

Constructional  Details — Owing  to  the  fact  that  in  an  all- 
spur  planetary  only  a  short  key  could  be  used  far  securing  the 
driving  pinion  to  its  shaft,  it  is  advisable  to  forge  this  pinion 
integral  with  the  shaft  so  as  to  avoid  possible  trouble  from  a 
loose  key.  In  the  older  designs  of  planetary  gears  the  planetary 
pinions  revolved  on  pins  supported  at  one  end  only.  This  con- 
struction leaves  much  to  be  desired,  for  the  reason  that  it  permits 
considerable  flexure  of  the  pinion  pins  and  leads  to  rapid  wear 
of  the  pinion  bushings,  and  consequent  noisy  operation.  A  spe- 
cially weak  point  often  found  in  connection  with  this  construc- 
tion was  the  method  of  fastening  the  pin  to  the  pinion  carrier. 
The  pin  was  somewhat  reduced  in  diameter  at  one  end,  and  the 
reduced  portion  was  threaded  to  screw  into  the  pinion  carrier. 
This  makes  the  section  of  the  pin  weakest  at  the  very  point  where 
the  maximum  stress  occurs.  It  is  much  preferable  to  turn  the 
pin  with  a  small  flange  to  provide  a  shoulder  for  the  joint,  and 
have  the  diameter  at  the  joint  the  same  as  inside  the  pinion. 
However,  pinion  pins  supported  at  both  ends  are  to  be  recom- 
mended in  every  case,  because  of  the  more  rigid  support  they 
give  to  the  pinions.  In  determining  the  diameter  of  the  pins  it  is 
advisable  to  calculate  the  stresses  occurring  in  them  under  full 
load,  and  the  deflection  produced  thereby. 

Brakes — In  the  design  of  the  brake  for  holding  rotary  parts 
stationary  for  the  low  speed  and  the  reverse,  efforts  should  be 
made  to  keep  down  the  radial  load  on  the  bearing  of  the  brake 
drum  due  to  the  brake  pull,  so  as  to  reduce  the  wear  of  that 
bearing.  It  is  quite  possible  to  entirely  eliminate  this  radial  load 
by  dividing  the  brake  bands  into  halves,  with  the  two  points  of 
anchorage  located  diametrically  opposite  on  the  brake  circle,  and 
dividing  the  brake  pull  equally  between  the  two  bands.  How- 
ever, owing  to  the  slightly  greater  complication  in  the  operating 
mechanism  this  is  never  done  in  practice.  One  manufacturer 
uses  disc  brakes  instead  of  band  brakes,  thereby  entirely  eliminat- 
ing radial  brake  load. 


144 


THE  PLANETARY  CHANGE  GEAR. 


Since  in  a  shaft  driven  car  the  axis  of  the  gear  lies  in  the 
direction  of  the  length  of  the  car  and  the  brake  operating  shaft 
transverse  thereto,  the  brake  bands  are  usually  operated  by 
means  of  face  cams,  as  illustrated  in  Fig.  91.  The  brake  band 
is  made  of  steel  and  lined  with  leather  or  fibre.  Lugs  are  riveted 
to  its  ends,  which  are  drilled  to  pass  over  the  operating  shaft. 


FIG.  91. — BRAKE  CONSTRUCTION  FOR  PLANETARY  GEAR. 

These  lugs  are  provided  with  cam  faces,  and  corresponding  face 
cams  are  secured  to  the  shaft,  so  that  when  the  latter  is  rotated 
in  a  particular  direction  the  ends  of  the  band  are  forced  together 
and  the  band  is  contracted  upon  the  drum.  A  coiled  spring  be- 
tween the  lugs  of  the  band  releases  the  latter  when  the  driver 
removes  his  foot  from  the  pedal  by  means  of  which  the  particu- 


THE  PLANETARY  CHANGE  GEAR. 


145 


lar  speed  is  engaged.  Any  wear  of  the  friction  lining  can  be 
compensated  by  adjustment  of  the  face  cams  on  their  shaft. 

One  common  fault  in  planetary  gears  is  that  the  brake  bands 
are  not  fully  released  but  drag  when  not  in  use.  To  prevent  this 
the  ends  of  the  band  should  be  allowed  considerable  motion,  and 
an  adjustable  set  screw  should  be  provided  at  a  point  opposite 
the  ends  of  the  band  to  act  as  a  stop  and  limit  the  release  motion 
at  that  point. 

In  some  planetary  gears  the  brakes  are  exposed,  but  it  is  cer- 
tainly preferable  to  enclose  the  entire  gear  inclusive  of  the  brakes. 


FIG.  92. — GEAR  AND  BEARING  PRESSURES  IN  AN  ALL-SPUR  PLAN- 
ETARY SET. 

Efficiency  of  Operation — Although,  so  far  as  the  author  has 
been  able  to  learn,  no  accurate  efficiency  tests  of  planetary  change 
speed  gears  have  ever  been  made,  this  type  of  gear  has  a  poor 
reputation  in  respect  to  efficiency.  Of  course  the  speeds  which 
involve  no  planetary  motion,  such  as  the  low  speed  in  a  simple 
"all-spur"  planetary  gear  (Fig.  87),  should  be  as  efficient  as  the 
corresponding  gear  in  a  sliding  gear  set,  provided  mechanical  de- 
sign and  workmanship  are  the  same.  But  the  efficiency  of  such 


146  THE  PLANETARY  CHANGE  GEAR. 

a  combination  as  that  of  the  reverse  in  an  all-spur  combination 
is  quite  low,  as  may  easily  be  shown.  The  losses  are  due  partly 
to  tooth  friction  and  partly  to  bearing  friction.  Such  a  combina- 
tion is  represented  diagrammatically  in  Fig.  92,  and  in  order  to 
somewhat  exaggerate  the  conditions  resulting  in  inefficient  opera- 
tion, the  two  planetary  pinions  are  shown  to  be  of  nearly  equal 
pitch  diameter.  The  gear  tooth  pressures  are  drawn  in  making 
an  angle  of  20  degrees  with  the  plane  of  the  gear  axes,  15  de- 
grees of  which  represent  the  tooth  flank  angle  and  5  degrees  the 
friction  angle.  We  found  in  the  previous  chapter  that  the  load 
on  the  bearing  of  a  spur  gear  is  equal  in  magnitude  and  direction 
to  the  load  on  the  gear  teeth,  and  since  the  two  planetary  pinions 
have  a  common  bearing,  we  can  transfer  the  tooth  pressures  to 
the  bearing  axis.  This  has  been  done  in  Fig.  92,  A  B  representing 
the  bearing  load  due  to  the  pressure  of  the  driving  pinion  and 
A  C  the  bearing  load  due  to  the  reaction  of  the  stationary  gear. 
A  D  is  the  resultant  of  these  two  and  represents  the  actual  load 
on  the  pinion  pin.  It  is  hardly  necessary  to  emphasize  the  fact 
that  a  pressure  in  the  direction  A  D  applied  to  the  pinion  pin 
does  not  act  very  advantageously  in  turning  the  pin  around 
centre  O.  This  pressure  can  be  resolved  into  two  components,  a 
radial  one  A  F  and  a  tangential  one  A  E.  The  latter  component 
represents  useful  turning  force  impressed  upon  the  pinion  carrier 
at  the  radius  of  the  pinion  pin  axis  with  the  driving  shaft  axis 
as  a  centre.  The  useful  work  is  proportional  to  this  force  or 
pressure,  which,  it  will  be  seen,  is  quite  small,  while  the  gear 
losses  are  proportional  to  the  much  greater  forces  A  B  and  A  C 
and  the  bearing  loss  in  the  pinion  pin  bearings  is  proportional  to 
A  D,  also  much  greater  than  A  E.  In  ordinary  spur  gearing  the 
power  transmitted  is  directly  proportional  to  the  tooth  pressure, 
as  are  all  of  the  losses.  In  the  above  planetary  combination  the 
tangential  (useful)  component  of  the  pinion  pin  load  becomes 
zero  as  the  two  planetary  pinions  become  equal. 

The  chief  advantage  of  the  planetary  gear  set  is  that  on  the 
direct  drive  it  consumes  absolutely  no  power,  having  no  bearings 
then  in  operation,  and  its  weight,  which  revolves,  adds  to  the 
flywheel  effect,  tending  to  steady  the  engine  motion.  This  ad- 
vantage can  be  made  the  most  of  on  cars  provided  with  relatively 
powerful  engines,  making  it  possible  to  drive  on  the  high  gear 
under  all  ordinary  road  conditions,  so  that  the  low  gear  is  needed 
only  in  starting  and  on  extremely  steep  hills. 


CHAPTER  V. 


THE  FRICTION  DISC  DRIVE. 

Types  of  Friction  Drives—Undoubtedly  the  simplest  of  all 
variable  transmission  mechanisms  for  gasoline  automobiles  is  the 
so  called  friction  drive.  There  are  several  types  of  frictional 
transmission  mechanisms,  and  they  may  be  roughly  classified  as 
follows :  Disc  and  wheel,  multiple  discs  and  wheels,  bevel  wheels, 
plain  wheels  and  grooved  wheels.  The  first  class  mentioned  is 
the  only  one  extensively  used.  This  change  speed  mechanism 
(A,  Fig.  93)  consists  of  a  disc  A  carried  on  an  extension  of  the 
engine  shaft,  and  of  a  mill  board  or  fibre-faced  friction  wheel  B, 
which  can  be  slid  along  a  cross  shaft  and  brought  into  frictional 
engagement  with  the  disc  A  at  a  greater  or  smaller  distance  from 
its  centre.  The  ratio  between  the  speeds  of  revolution  of  wheel 
and  disc  is  substantially  equal  to  the  reciprocal  of  the  ratio  be- 
tween the  diameter  of  the  wheel  and  the  diameter  of  the  mean 
contact  circle  on  the  disc.  By  moving  the  wheel  from  the  centre 
of  the  disc  outward  the  speed  of  the  wheel  can  be  changed  from 
nothing  to  the  maximum  by  infinitesimal  increments,  and  by 
sliding  the  wheel  over  to  the  opposite  side  of  the  disc  its  direc- 
tion of  motion  may  be  reversed.  Before  the  wheel  is  slid  in  the 
direction  of  its  axis  it  must  be  disengaged  from  the  disc,  which 
is  accomplished  either  by  moving  the  bearings  of  the  cross  shaft  in 
planes  perpendicular  to  their  axis  or  by  moving  the  bearing  directly 
behind  the  disc  in  the  direction  of  its  axis.  After  the  wheel  has 
been  slid  to  the  desired  position,  wheel  and  disc  are  again  brought 
into  frictional  engagement  by  the  reverse  operation.  This  so 
called  friction  disc  drive,  therefore,  serves  not  only  as  a  speed 
changing  and  reversing  gear,  but  also  performs  the  function  of  a 
friction  clutch.  It  possesses  a  number  of  advantages,  viz.,  ex- 
treme simplicity,  low  cost  of  construction  and  maintenance,  abso- 
lutely silent  operation,  and  the  fact  that  it  furnishes  an  unlimited 
number  of  speed  gradations.  Among  the  weak  points  of  this 
transmission  are  the  unavoidable  loss  of  power  due  to  slipping  at 

147 


148  THE  FRICTION  DISC  DRIVE. 

the  contact  surfaces  and  the  fact  that  the  frictional  conditions 
are  impaired  by  oil,  mud,  etc.,  on  the  frictional  surfaces.  Owing 
to  the  necessary  bulk  of  this  mechanism  it  is  impossible  to  prop- 
erly enclose  it. 

Before  taking  up  the  technical  discussion  of  this  drive  it  will 
be  well  to  briefly  describe  some  of  the  numerous  varieties  of 
friction  transmissions  used  in  automobile  work.  Most  of  the 
drives  described  in  the  following  have  been  used  only  in  single 
cases,  ana  none  can  be  regarded  as  in  common  use  in  the  industry. 

B  in  Fig.  93  illustrates  a  drive  consisting  of  two  oppositely 
located  friction  discs  and  two  friction  wheels  between  them. 
Each  wheel  is  in  frictional  contact  with  one  disc  only,  and  each 
has  a  separate  drive  to  one  of  the  rear  road  wheels.  It  will  be 
noted  that  one  of  the  cross  shafts  is  set  slightly  farther  to  the 
rear  than  the  other,  so  that  each  wheel  may  contact  with  one 
disc  and  clear  the  other.  As  compared  with  the  single  disc  drive 
the  construction  has  the  advantage — purchased  at  the  cost  of 
some  complication — that  the  over-all  dimensions  for  a  certain 
transmission  capacity  are  less  and  that  the  need  of  a  differential 
gear  is  dispensed  with.  At  least  no  differential  is  used  with  this 
construction,  although  it  would  seem  that  the  certainty  of  steering 
might  be  somewhat  affected  by  its  absence. 

At  C  is  shown  the  Seitz  design  of  friction  drive,  which  com- 
prises a  single  disc  and  two  pairs  of  friction  wheels,  oiie  pair  on 
either  side  of  the  disc.  Each  friction  wheel  has  its  individual 
shaft,  and  by  means  of  a  suitable  linkage  the  bearings  of  the 
shafts  to  one  side  of  the  centre  of  the  disc  can  be  moved  together 
so  the  wheels  on  them  will  pinch  the  disc,  thus  establishing  fric- 
tional driving  connection  with  it.  One  pair  of  wheels  serves  for 
the  forward  drive  and  the  other  for  the  reverse,  the  latter  pair 
being  fixed  on  their  respective  shafts,  thus  giving  only  a  single 
reverse  reduction.  Power  is  transmitted  to  a  transverse  jack- 
shaft  by  means  of  roller  chains  which  run  over  sprockets  on  each 
of  the  two  friction  wheel  shafts  corresponding  to  one  direction 
of  motion.  The  chief  advantage  of  this  construction  is  that  there 
is  no  end  thrust  on  the  disc  and  its  shaft,  hence  no  provision 
need  be  made  to  take  it  up  on  thrust  bearings,  and  there  is  no 
chance  of  the  frame  being  distorted  by  the  "off  centre"  pressure 
on  the  disc. 

The  arrangement  illustrated  at  D  combines  a  direct  drive  for 
yuse  under  all  ordinary  road  conditions.  For  slow  speed  and  re- 
Verse  operation  the  power  is  transmitted  from  the  driving  disc  A 
(which  may  be  the  engine  flywheel)  to  the  two  fraction  wheels 


THE  FRICTION  DISC  DRIVE. 


149 


BB,  and  thence  to  the  friction  whqel  C,  which  is  slidably  mounted 
on  the  driven  shaft.  Wheel  C  is  shown  in  the  position  corre- 
sponding to  the  reverse  motion.  Pushing  it  toward  the  driving 
disc  past  the  centres  of  wheels  BB  gives  the  forward  motion,  the 
speed  gradually  increasing  until  wheel  C  is  close  to  the  driving 
disc  A.  Then  the  side  wheels  BB  are  moved  apart  out  of  contact 
with  wheel  C,  and  the  forward  conical  projection  of  the  latter  is 
forced  into  a  conical  recess  formed  in  the  flywheel  rim,  these 


FIG.  93. — TYPES   OF  CONTINUOUSLY  VARIABLE   FRICTION   DRIVES. 

parts  acting  as  a  cone  clutch  and  connecting  the  driven  to  the 
driving  shaft  for  the  direct  drive.  This  obviates  the  frictional 
loss  inherent  in  the  operation  of  the  disc  and  wheel  and  also 
makes  the  drive  positive. 

In  all  of  the  friction  drives  so  far  described  the  transmission 
ratio  is  continuously  variable.  However,  there  are  other  fric- 
tional drives  which  do  not  possess  this  feature  of  an  "infinite 


150 


THE  FRICTION   DISC  DRIVE 


number  of  gear  changes,"  giving  generally  only  two  forward 
speeds. 

These  change  gears  are  used  on  account  of  their  simple  con- 
struction and  quiet  operation.  Among  these  is  the  friction  cone 
type,  shown  at  A  in  Fig.  94.^  This  drive  comprises  two  driven 
members  C  with  double  conical  friction  surfaces  and  three  driv- 
ing cones  A,  B  and  R,  all  mounted  slidably  on  a  feathered  driv- 
ing shaft.  A  gives  the  high  speed  forward,  B  the  low  speed  for- 
ward, and  R  the  reverse,  engagement  being  effected  by  moving 
the  driving  cones  axially  into  contact  with  the  driven  cones. 

Counterparts  of  sliding  and  planetary  change  speed  gears  con- 
taining friction  wheels  instead  of  gear  pinions  have  also  been 


\  R 


FIG.  94. — TYPES  OF  STEPPED  FRICTION   DRIVES. 

used,  but  have  been  discarded.  B,  Fig.  94,  illustrates  the  grooved 
friction  wheel  drive  used  by  Charles  E.  Duryea  on  light  vehicles. 
Less  normal  pressure  between  wheels  is  required  when  the 
frictional  surfaces  are  formed  with  V  grooves  than  when  they 
are  smooth,  but  to  balance  this  there  is  somewhat  greater  loss 
at  these  surfaces. 

Materials— The  disc  of  a  friction  disc  drive  always  has  a 
metallic  surface.  Aluminum  is  claimed  to  possess  superior  fric- 
tional qualities  and  is  used  by  one  concern  manufacturing  fric- 
tion driven  automobiles,  which  has  a  patent  on  its  use  for  this 
purpose.  However,  cast  iron  is  also  successfully  used.  The 
•wheels  are  always  faced  with  some  kind  of  fibrous  material 
which  is  more  or  less  compressible  and  has  a  relatively  high 
coefficient  of  friction  in  contact  with  metal.  Mill  board  is 


THE  FRICTION  DISC  DRIVE. 


151 


commonly  employed,  and  is  sometimes  indurated  with  a  tarry 
substance  to  improve  its  frictional  qualities.  The  friction  co- 
efficient between  cast  iron  and  mill  board  under  ordinary  con- 
ditions varies  between  0.25  and  0.30.  The  facing  material  is 
cut  into  rings  which  are  assembled  between  steel  flanges. 

Theoretical  Efficiency — It  is  obvious  that  the  motion  of  the 
wheel  rim  on  the  face  of  the  disc  cannot  be  a  pure  rolling  motion, 
since  both  sides  of  the  wheel  have  the  same  circumference, 
whereas  the  outer  circumference  of  the  contact  ring  on  the  disc 
is  considerably  longer  than  the  inner  circumference.  This  con- 
dition entails  sliding  motion  and  consequent  frictional  loss.  An 
analytical  investigation  of  this  loss  has  been  made  by  Professor 


FIG.  95. 

Benjamin  Bailey   (THE  HORSELESS  AGE,  July  6,   1910),   whose 
method  we  may  here  follow. 

Referring  to  Fig.  95,  let  n  be  the  inner  and  rz  the  outer 
radius  of  the  contact  ring  on  the  disc.  Imagine  that  the  disc 
is  stationary  and  that  the  wheel  rolls  around  it.  A  little  con- 
sideration will  show  that  the  total  slippage  during  one  revolu- 
tion will  be  the  same  as  if  the  wheel  were  rotated  once  around 
the  centre  point  of  contact  on  the  disc.  This  occurs  when  the 
wheel  is  at  the  entre  of  the  disc.  Let  P  be  the  frictional  force 
on  the  circumference  of  the  wheel,  and  let  it  be  supposed  that 
the  normal  pressure  between  disc  and  wheel  is  just  sufficient 


152 


THE  FRICTION  DISC  DRIVE. 


to  prevent  slippage  of  the  wheel, 
in  width  of  the  contact  ring  then  is 


The  frictional  force  per  inch 

p 
pounds.     In  Fig. 


96  the  circle  of  diameter  t  represents  the  whole  area  over  which 
the  slipping  takes  place.  Imagine  that  the  wheel  is  stationary 
at  the  centre  of  the  disc  and  that  the  latter  is  turning  under 
it  When  the  disc  then  makes  one  complete  revolution,  every 
portion  of  the  circle  of  diameter  t  is  passed  over  twice  by  an 
element  of  the  wheel  circumference.  Now,  consider  an  infinitesi- 


-t-rrr2 
FIG.  96. 

mal  ring  of  width  dr.  If  W  represents  the  frictional  work  done 
on  the  entire  circle  during  one  revolution,  then  the  work  done 
on  the  ring  dr  is 

P 


irr  dr. 


—  r\ 


Integrating  this  between  the  limits  r  =  o  and  r=  (ra  —  n)/2  we 
get 


This,  therefore,  represents  the  power  lost  in  friction  during 


THE  FRICTION  DISC  DRIVE.  153 

each  revolution  of  the  disc.  The  useful  work  transmitted  dur- 
ing one  revolution  is  ri  -j-  r2 

2  TT  p =  TT  p  (ri  +  r.) 

2 
hence  the  efficiency  is  •*  p  (ri  +  r2) 

e  =  , 

7TP 

TP(rx  +  r,)  + (r2  —  n), 

which  may  be  reduced  to    2  (r±  +  r8) 

3  r,  +  n 

Let  f  be  the  width  of  contact  of  the  wheel  and  r  the  radius  from 
the  centre  of  the  disc  to  the  middle  point  of  contact,  then  the 
formula  for  the  efficiency  may  be  written 

e    =    (33) 

t 

1  +  — 

4r 

With  a  width  of  contact  equal  to  1^  inches  and  a  mean 
radius  of  contact  of  9  inches  (typical  of  high  speed  operation 
on  a  moderate  sized  car),  the  efficiency  figures  out  to  about  96 
per  cent.  With  a  mean  radius  of  contact  of  3  inches  (low  gear) 
the  efficiency  figures  out  to  88.8  per  cent. 

In  actual  practice  the  normal  pressure  between  disc  and  wheel 
is  always  greater  than  that  required  to  just  keep  the  wheel  from 
slipping,  and  may  be  far  greater.  This,  of  course,  will  propor- 
tionately increase  the  loss  due  to  slippage.  If  the  ratio  of  the 
actual  normal  pressure  to  that  required  to  just  prevent  slippage 
be  k,  then  the  efficiency  is 

e  =  (34) 

kt 

1+ • 

4r 

This  efficiency,  moreover,  is  only  an  ideal  efficiency,  not  taking 
account  of  bearing  losses  and  any  slippage  there  may  be  beyond 
that  required  by  the  difference  in  the  lengths  of  the  inner  and 
outer  circumference  of  the  contact  ring  on  the  disc. 

Dimensions  of  Disc  and  Wheel. — From  equation  (33)  it  will 
be  seen  that  the  efficiency  increases  with  the  mean  radius  of  con- 
tact and  as  the  width  of  contact  decreases.  Hence  it  is  desirable 
to  use  as  large  a  disc  as  constructional  limitations  permit  and 
make  the  wheel  as  narrow  as  the  rigidity  and  wearing  qualities 
of  the  facing  will  allow  of.  For  pleasure  cars  a  disc  diameter  of 
20  inches  is  about  the  limit,  because  the  motor  must  be  located 


154  THE  FRICTION  DISC  DRIVE. 

low  for  the  sake  of  stability,  and  yet  a  ground  clearance  of 
about  10  inches  must  be  maintained.  In  commercial  cars,  in 
which  the  power  plant  can  be  placed  somewhat  higher,  the  disc 
may  be  as  large  as  24  inches  in  diameter.  The  wheel  is  gener- 
ally made  of  about  the  same  diameter  as  the  disc,  so  that  when 
it  is  in  the  position  farthest  from  the  centre  of  the  disc  the 
power  is  transmitted  without  change  of  speed. 

Suppose  that  a  friction  drive  is  to  be  designed  for  a  four  cylin- 
der 4x5  inch  touring  car.    The  disc  would  be  made,  say,  20  inches 
in  diameter  and  the  friction  wheel  rim  134  inches  wide.     This 
would  make  the  mean  radius  of  the  contact  ring,  with  the  wheel 
in  the  extreme  high  speed  position,  9l/&  inches.     The  above  men- 
tioned motor  develops  a  normal-speed  torque  of  108  pounds-feet. 
Hence  the  force  to  be  transmitted  at  a  radius  of  9J4  inches  is 
12  X  108 
— =    142   pounds, 

.   ?** 
and  figuring  on  a  friction  coefficient  of  0.3,  the  necessary  normal 

pressure   is  142 

=   473   pounds. 

0.3 

On  the  other  hand,  the  friction  device  must  also  be  capable  of 
transmitting  the  full  power  of  the  motor  when  the  wheel  is  at 
only,  say,  3  inches  mean  distance  from  the  centre  of  the  disc,  for 
low  speed  operation.  The  frictional  force  then  is 
12  X  108 
=  432  pounds, 

o 

and  the  required  normal  pressure 
432 

=  1440  pounds. 

0.3 

Hence  the  mechanism  for  applying  the  wheel  to  the  surface  of 
the  disc  must  enable  the  driver  to  exert  at  least  this  pressure. 

It  is  obvious  that  the  torque  which  may  be  transmitted  by  a 
friction  wheel  and  disc  is  directly  proportional  to  the  diameter 
of  the  disc,  and  it  also  increases  with  the  width  of  face  of  the 
wheel,  provided  the  latter  is  not  too  large.  In  determining  the 
dimensions  it  is  well  to  make  the  disc  as  large  in  diameter  as 
is  permissible  from  the  viewpoints  of  height  of  centre  of  gravity 
and  ground  clearance  required,  and  then  give  the  wheel  a  width 
of  face 

/  =  — ..  (35) 

4D 
where  T  is  the  maximum  torque  of  the  motor  (Table  1)  and  D 


THE  FRICTION  DISC  DRIVE 


155 


the  outside  diameter  of  the  disc.    In  no  case  should  /  be  greater 

D 

than  — . 
10 

Wheel  Sliding  Mechanism. — The  friction  wheel  is  arranged 
on  a  cross  shaft  either  of  the  fluted  type  or  provided  with  one  or 
more  long  keys.  The  hub  of  the  wheel  is  formed  with  a  groove 
for  a  sliding  collar  for  connection  to  the  operating  lever.  Owing 
to  the  great  range  of  motion  of  the  wheel,  long  armed  levers 
must  be  employed  in  the  operating  mechanism.  Fig.  97  illus- 
trates a  typical  arrangement  of  this  mechanism.  The  position 


FIG.  97. — WHEEL  SLIDING  MECHANISM. 

of  the  friction  wheel  is  controlled  by  a  hand  lever  moving  over 
a  notched  quadrant. 

Friction  driven  cars  practically  always  have  a  final  drive  by 
chain,  either  one  or  two  chains  being  used.  With  the  single 
chain  the  sprocket  pinion  is  fixed  to  the  shaft  of  the  friction 
wheel  just  beyond  the  range  of  motion  of  the  wheel  on  the  re- 
versing side,  and  the  shaft  is  carried  in  bearings  secured  to  the 
frame  side  members.  With  the  double  chain  drive  the  differen- 
tial gear  must  be  incorporated  in  the  cross  shaft.  The  friction 


156 


THE  FRICTION   DISC  DRIVE. 


wheel  then  slides  on  a  hollow  shaft  which  is  secured  to  the 
housing  of  the  differential  gear,  the  cross  shaft  proper  being 
divided  and  each  part  fastened  to  one  side  gear  of  the  differential. 
There  should  be  an  extension  of  the  hollow  shaft  beyond  the 
differential  so  that  this  shaft  may  be  supported  in  bearings  hung 


FIG.  98. — MOUNTING  FOR  WHEEL  AND  Disc  SHAFTS. 
(JAKOB'S  DESIGN.) 

from  the  side  frame  members,  which  relieves  the  differential  or 
inner  shafts  of  much  strain. 

Means  for  Engaging  Wheel  and  Disc — Considerable  im- 
portance attaches  to  the  method  of  mounting  the  bearings  for 
the  disc  shaft  and  of  taking  up  the  various  stresses  due  to  the 
normal  pressure  between  the  disc  and  wheel.  As  has  already 
been  shown,  these  stresses  are  of  considerable  magnitude,  and 
they  may  produce  serious  distortions  of  the  frame  unless  suit- 
able means  are  provided  for  taking  them  up.  Fig.  98  illustrates 
a  design  due  to  Victor  Jakob.  The  cross  shaft  is  supported  in 


THE  FRICTION  DISC  DRIVE. 


157 


two  brackets  riveted  to  the  frame,  being  provided  with  ball  bear- 
ings mounted  in  spherical  housings.  If  required  for  renewing  the 
facing  of  the  wheel,  the  cross  shaft  can  easily  be  removed  toward 
the  rear  after  the  caps  have  been  taken  off. 

In  order  to  avoid  twisting  of  the  frame  side  members,  due  to 
the  reactions  between  disc  and  wheel,  the  bearings  are  placed 
close  to  the  frame  and  the  axis  of  the  shaft  intersects  the  neu- 
tral axis  of  the  frame  member.  This  arrangement  necessitates 
a  somewhat  higher  location  of  the  motor  than  customary  with 
gear  drives,  but  this  is  required,  anyhow,  in  order  to  obtain  the 
necessary  road  clearance  under  the  disc  and  wheel. 

From  each  of  the  cross  shaft  bearing  brackets  a  tension  rod 


f=n  -  = 


FIG.  99. — CAM  MECHANISM  FOR  APPLYING  Disc  TO  WHEEL. 

is  run  straight  forward  to  a  cross  member  which  is  riveted  to 
the  frame.  The  centre  part  of  this  cross  member  is  widened  out 
and  has  a  hole  in  the  web  so  as  to  accommodate  a  barrel  which 
serves  as  a  support  for  the  disc  shaft,  the  barrel  being  fastened 
to  the  cross  member  by  an  integral  flange.  The  front  end  of 
the  barrel  is  supported  on  another  cross  member  by  means 
which  permit  of  raising  or  lowering  this  end,  whereby  the  disc 
shaft  and  the  cross  shaft  can  be  leveled  up  properly.  Their  con- 
tinued perpendicularity  is  assured  by  two  tie  rods  which  run 
diagonally  from  the  front  end  of  the  barrel  to  the  point  at  which 
the  parallel  tie  rods  are  connected  to  the  cross  member. 

The  disc  shaft  is  carried  in  the  barrel  on  two  ball  bearings, 
the  one  near  the  disc  being  of  a  combined  radial  and  thrust  type, 
so  as  to  be  able  to  take  the  end  thrust  due  to  the  pressure  of 
engagement.  Only  little  end  thrust  has  to  be  taken  up  on  the 


158 


THE  FRICTION   DISC  DRIVE. 


forward  bearing,  viz.,  that  due  to  the  disengaging  spring,  one  end 
of  which  rests  against  the  outer  race  of  this  bearing,  while  the 
other  end  rests  against  a  shoulder  in  the  barrel.  The  bearings 
are  rigidly  secured  to  the  shaft  and  their  outer  races  slide  in  the 
housing  when  the  disc  and  wheel  are  engaged  and  disengaged. 

The  disc  shaft  is  coupled  to  the  motor  by  a  floating  shaft  hav- 
ing a  universal  joint  at  either  end,  one  of  which  joints  also  has 


FIG.   100. — DIAGRAM  OF  REACTIONS  DUE  TO  PRESSURE  OF 
APPLICATION. 


a  sliding  motion.  Engagement  of  the  friction  members  is  ef- 
fected by  two  cams,  one  on  either  side  of  the  barrel  (Fig.  99). 
These  cams  form  an  integral  piece  with  a  lever,  which  is  con- 
nected to  a  pedal  operated  in  the  usual  manner  by  the  driver. 
The  cams,  which  are  shaped  according  to  a  certain  curve,  press 
against  rollers  mounted  on  studs  which  project  through  slots  in 
the  barrel.  The  studs  are  screwed  into  a  sleeve  adapted  to  slide 


THE  FRICTION  DISC  DRIVE.  159 

inside  the  barrel  and  resting  against  the  baM  bearing  arrange- 
ment which  carries  the  rear  end  of  the  disc  shaft.  The  slots 
through  which  the  roller  studs  project  are  sufficiently  wide  to 
permit  a  slight  degree  of  rotation  of  the  sleeve,  by  which  the 
contact  of  both  cams  with  their  rollers  is  insured. 

A  special  feature  of  Mr.  Jakob's  design  is  that  the  reactions 
caused  by  the  engagement  of  the  friction  mechanism  are  taken 
up  entirely  within  a  truss  and  tie  rod  system,  with  the  exception 
of  the  pull  on  the  cam  lever  exerted  by  the  driver.  This  force, 
however,  is  not  very  large,  and  is  well  taken  care  of  by  the  diag- 
onals and  two  cross-members.  That  the  remaining  forces  are 
completely  taken  up  within  the  system  is  shown  by  the  diagram 
Fig.  100.  In  drawing  this  diagram  it  was  assumed  that  in  engag- 
ing the  disc  and  wheel  at  the  point  of  maximum  speed  the  driver 
applied  to  the  pedal  the  pressure  necessary  to  hold  the  two  in 
engagement  in  the  position  of  low  speed  under  full  engine  power, 
viz.,  1,440  pounds.  Compression  and  tension  are  indicated  by 
arrow  heads  turned  toward  each  other  for  the  former,  and  away 
from  each  other  for  the  latter. 

One  of  the  possible  troubles  with  a  friction  disc  drive  that 
should  be  provided  against  is  that  of  wearing  flats  on  the  wheel 
by  allowing  the  disc  to  slip  for  extended  periods  on  using  the 
gear  as  a  brake.  Manufacturers  formerly  sometimes  recom- 
mended the  use  of  the  friction  transmission  for  braking  purposes, 
but  this  practice  is  to  be  condemned.  Of  course,  only  an  inex- 
perienced driver  will  cause  the  disc  to  slip  for  a  long  time  on  a 
stationary  wheel, 


CHAPTER  VI. 


UNIVERSAL  AND   SLIP  JOINTS. 

Universal  joints  serve  the  purpose  of  connecting  shafts  or  con- 
trol rods  whose  axes  lie  in  the  same  plane  but  make  an  angle 
with  each  other.  They  are  particularly  required  when  the  angle 
between  the  shafts  varies  in  service.  In  an  automobile  the  most 
important  application  of  universal  joints  is  in  the  transmission 
line  between  the  spring-supported  parts  and  those  carried  by  the 
driving  axle.  Every  shaft  driven  car  must  have  at  least  one 
universal  joint  in  the  propeller  shaft,  and  many  have  two. 

The  simplest  form  of  universal  joint  consists  of  a  squared 
block  secured  to  one  of  the  shafts  to  be  connected,  fitting  in  a 
square  hole  in  a  sleeve  secured  to  the  other  shaft.  The  four 
faces  of  the  block  are  curved  in  the  direction  of  the  axis  of  the 
shaft  to  which  the  block  is  fastened.  This  type  of  universal  joint 
is  illustrated  in  Fig.  101.  It  will  'readily  be  seen  that  owing  to 
the  curvature  of  the  faces  of  the  block,  one  of  the  shafts  can  be 
moved  angularly  with  relation  to  the  other  in  two  planes  at 
right  angles  to  each  other.  This  joint  also  constitutes  a  slip  joint. 

The  prototype  of  the  modern  universal  joint  is  the  Hooke  or 
Cardan  joint,  illustrated  in  Fig.  102.  It  consists  of  two  forks, 
each  of  which  is  secured  to  one  of  the  shafts  to  be  connected,  and 
of  a  cross-shaped  part  which  is  connected  to  each  of  the  forks 
by  means  of  a  pin.  In  the  form  here  illustrated  and  as  used  in 
stationary  work,  the  axes  of  the  two  pins  do  not  intersect,  but 
are  at  some  distance  from  each  other  to  allow  of  the  pins  passing 
each  other.  However,  there  is  an  advantage  in  having  the  pins 
both  in  the  same  plane.  This  end  can  be  attained  by  using  pins 
of  different  diameters  and  passing  one  through  the  other,  or  by 
using  one  long  and  two  short  pins.  Cardan  joints  thus  modified 
are  used  in  automobile  work.  In  the  design  illustrated  one  pin 
locks  the  other  in  position  and  is  itself  locked  by  a  cap  screw 

160 


UNIVERSAL  AND  SLIP  JOINTS 


161 


FIG.  101. — SQUARE  BLOCK  TYPE  OF  UNIVERSAL  AND  SLIP  JOINT. 


through  one  arm  of  the  cross  and  passing  beneath  the  surface  of 
the  pin. 

A  design  in  which  the  cross  is  replaced  by  a  ring  is  illustrated 
in  Fig.  103.  This  also  comprises  two  forks,  but  instead  of  the 
outer  ends  of  the  forks  having  radial  bearing  holes  drilled  through 
them,  they  are  provided  with  bearing  pins  extending  radially 
outward.  The  ring  has  bearings  for  these  pins  formed  in  it.  It 
is  made  in  halves,  being  split  through  the  centre  lines  of  the  four 
bearings  so  as  to  permit  of  assembling  the  joint.  The  halves 
are  secured  together  by  means  of  cap  screws  and  nuts. 

A  slight  variation  from  the  design  just  described  consists  in 
a  ring  formed  with  four  radial  bearing  pins  and  forks  with  sepa- 
rate bearing  caps,  as  illustrated  in  Fig.  104.  This  type  offers 
particular  advantages  when  the  universal  joint  is  to  be  secured 
to  a  brake  drum,  clutch  drum  or  similar  member,  as  only  one 


FIG.    102.— CROSS    TYPE   OF   UNIVERSAL   JOINT. 


162 


UNIVERSAL  AND  SLIP  JOINTS. 


FIG.  103. — SPLIT  RING  TYPE  OF  UNIVERSAL  JOINT. 

fork  is  required  in  that  case,  the  part  of  the  other  fork  being 
taken  by  a  pair  of  lugs  cast  integral  with  the  web  of  the  brake 
drum,  etc.  This  is  shown  in  the  illustration.  Again,  one  member 
may  be  made  in  the  form  of  a  disc  keyed  to  the  driving  shaft, 
which  forms  part  of  the  universal  joint  housing. 

Probably  the  most  extensively  used  type  of  universal  joint  is 
the  slotted  shell  and  trunnion  block  type,  illustrated  in  Fig.  105. 
This  consists  of  a  cup-shaped  steel  forging  secured  to  one  of  the 
shafts,  with  two  diametrically  opposite  longitudinal  slots  milled 


FIG.  104.— INTERNAL  RING  TYPE  OF  JOINT. 


UNIVERSAL  AND  SLIP  JOINTS. 


163 


FIG.  105. — BLOCK  AND  TRUNNION  TYPE  UNIVERSAL  JOINT. 

in  its  shell.  The  other  shaft  is  provided  with  a  ball  shaped  end 
fitting  the  interior  of  the  shell  and  provided  with  pins  or  studs 
extending  into  the  slots.  Hardened  steel  trunnion  blocks  are  in- 
terposed between  the  pins  and  the  walls  of  the  slots  to  distribute 
the  bearing  pressure.  This  type  of  joint,  it  will  be  noted,  serves 
also  as  a  slip  joint,  and  it  can  be  easily  enclosed. 

Periodical  Speed  Fluctuations. — A  feature  of  all  of  the 
universal  joints  described  above  is  that  they  do  not  transmit  mo- 
tion uniformly  when  the  shafts  are  at  an  angle  with  each  other; 
that  is  to  say,  if  the  driving  shaft  runs  at  uniform  speed,  the  speed 
of  the  driven  shaft  will  vary  periodically,  being  soon  less  and 
soon  greater  than  the  speed  of  the  driving  shaft.  The  common 
feature  of  all  of  these  joints  is  that  they  have  two  rocking  axes 
at  right  angles  to  each  other. 

To  gain  an  idea  of  the  magnitude  of  the  variation  in  angular 
velocity,  we  will  assume  a  universal  joint  connecting  two  shafts 


FIG.  106. 


164  UNIVERSAL  AND  SLIP  JOINTS. 

in  a  vertical  plane,  the  driving  shaft  being  placed  horizontally, 
as  in  Fig.  106.  The  axes  of  the  two  pins  intersect  each  other, 
their  ends  being  designated  by  AA  and  BE,  respectively.  When 
the  joint  is  in  motion  the  line  A  A  describes  a  circle  in  a  vertical 
plane,  and  the  line  BB  a  circle  in  a  plane  making  with  the  vertical 
an  angle  <t>,  equal  to  the  angle  between  the  two  shafts.  These  two 
circles  are  great  circles  of  the  same  sphere,  the  common  diameter 
being  a  line  through  the  point  C  perpendicular  to  the  paper. 
Points  A  and  B  always  remain  at  the  same  distance  from  each 
other,  viz.,  one  quadrant  of  a  great  circle.  The  deviation  in  the 
direction  of  travel  is  the  greatest  when  either  point  A  or  point 
B  coincides  with  the  points  of  intersection  of  the  great  circles. 
When  the  points  A  coincide  with  these  points  of  intersection,  the 
angular  speed  of  the  driven  shaft  is  smaller  than  the  angular 
speed  of  the  driving  shaft,  and  when  points  B  coincide  with  these 
points  of  intersection  the  angular  speed  of  the  driven  shaft  is 
greater  than  the  angular  speed  of  the  driving  shaft.  There  are 
four  points  in  each  revolution  in  which  driving  and  driven  shafts 
rotate  at  equal  angular  speeds,  these  being  located  substantially 
midway  between  the  points  of  maximum  and  minimum  speeds 
of  the  driven  shaft. 

Let  the  two  large  arcs  in  Fig.  107  represent  the  great  circles  in 
which  the  points  A  and  B  travel.  Let  point  A  travel  from  the 
point  of  intersection  to  point  A'  and  point  B  travel  at  the  same 
time  to  B',  which  is  determined  by  the  fact  that  A'  B'  must  be  a 
quadrant.  Now,  lay  off  from  the  point  B'  on  the  line  of  travel 
of  point  B  a  quadrant,  or  90  degrees,  which  will  give  point  C. 
Through  A'  and  C  draw  an  arc  of  a  great  circle.  Angles  B'  A' 
C  and  B'  C  A'  are  both  right  angles  (because  their  opposite  sides 
are  quadrants),  hence  angle  A  C  A'  is  a  right  angle.  We,  there- 
fore, have  a  right-angled  spherical  triangle  A  A'  C,  the  angle  A' 
A  C  of  which  is  equal  to  the  angle  between  the  two  connected 
shafts,  the  side  AA'  of  which  represents  the  angular  motion  of 
the  driving  shaft,  and  the  side  A  C  the  angular  motion  of  the 
driven  shaft  during  a  short  period  after  the  point  A  has  passed 
through  the  point  of  intersection;  in  other  words,  when  the  pin 
of  the  driving  shaft  is  at  right  angles  to  the  plane  through  the 
two  connected  shafts. 

According  to  a  theorem  of  spherical  trigonometry 

cos  A'AC  =  tan   A  C  cot  A  A' (36) 

Since  the  tangent  is  the  reciprocal  of  the  cotangent  we  may 
write  this 

tan  AC       cosA,AC, 
t^nA  A' 


UNIVERSAL  AND  SLIP  JOINTS. 


165 


and  since  for  very  small  angles  the  tangents  are  proportional  to 
their  angles,  we  have 
A  C 


A  A' 


=  cos  A' A  C. 


(37) 


Therefore,  when  the  pin  of  the  driving  shaft  is  perpendicular  to 
the  plane  through  the  connected  shafts  the  angular  velocity  of 
the  driven  shaft  is  smaller  than  the  angular  velocity  of  the  driv- 
ing shaft  in  the  proportion  of  the  cosine  of  the  angle  between  the 
two  shafts  to  unity.  It  may  be  shown  in  a  similar  way  that  when 
the  pin  on  the  driving  shaft  is  in  the  plane  of  the  two  connected 


FIG.  107. 

shafts  the  driven  shaft  runs  faster  than  the  driving  shaft  in  the 
inverse  proportion. 

It  is  also  of  interest  to  find  an  expression  for  the  momentary 
ratio  of  angular  velocities  at  any  point  in  the  revolution  of  the 
driving  shaft.  To  simplify  the  expressions,  we  will  denote  the 
angle  A'  A  C  by  <£,  the  side  A  A'  by  a  and  the  side  A  C  by  b. 
Then  we  have  as  betore  (liquation  36) 
tan  b  =  cos  (f>  tan  a (38) 


166  UNIVERSAL  AND  SLIP  JOINTS. 

Differentiating,  we  have 

sec2  b  db  =  cos  <t>  sec2  a  da 
and 

db                   sec2  a 
=  cos  0 1 , (39) 

da  sec2  b 

which  gives  the  ratio  of  angular  velocities  at  any  moment  in 
terms  of  0,  a  and  b.  It  is  preferable,  however,  to  express  the 
value  in  terms  of  0  and  a  only,  as  b  is  not  directly  known,  and 
the  latter  can  be  easily  eliminated.  Squaring  equation  (38)  we 
have 

tan2  b  =  cos2  <t>  tan2  a. 
Adding  1  to  each  side  of  the  equation — 

1  +  tan2  b  =  1  +  cos2  <t>  tan2  a (40) 

But  since 

1  +  tan2  b  =  sec2  b} 

we  may  substitute  the  right  hand  term  of  equation  (40)  for  sec*  b 
in  equation  (39) 
db  sec2  a 

—  =  cos<t> . , (41 ) 

da  1  +  cos2  <j>  tan2  a 

which  gives  the   ratio   of   angular  velocities  after  any  angular 
move  a  of  the  driving  shaft  from  the  zero  position  in  which  the 
pin  of  the  driving  fork  is  perpendicular  to  the  plane  through  the 
two  shafts.     When  a  =  o  equation   (41)   reduces  to 
db 

=  COS  0. 

da 

which  is  the  same  as  already  found  for  the  position  of  minimum 
speed  of  the  driven  shaft. 

The  curve,  Fig.  108,  shows  the  variation  in  speed  of  the  driven 
shaft  during  a  motion  of  one-half  a  revolution  or  180  degrees 
the  driving  shaft  making  1,000  r.  p.  m.  and  the  angle  between  the 
shafts  (0)  being  30  degrees.  We  start  with  the  position  where 
the  pin  of  the  driving  fork  is  perpendicular  to  the  plane  of  the 
two  shafts.  In  this  position  the  driven  shaft  rotates  at  the  rate 
of  866  r.  p.  m.,  its  lowest  speed.  The  speed  of  the  driven  shaft 
increases  until  after  a  little  more  than  45  degrees  motion  of  the 
driving  shaft  it  equals  the  speed  of  the  latter.  It  keeps  on 
increasing,  and  after  90  degrees  motion,  when  the  pin  of  the 
driving  fork  is  in  the  plane  of  the  connected  shafts,  it  attains  its 
maximum  speed  of  1,155  r.  p.  m..  Then  it  decreases  again,  ac- 
cording to  the  same  curve,  until  after  180  degrees,  or  one-half 
revolution,  it  again  attains  its  minimum  speed  of  866  r.  p.  m.  Dur- 
ing one  revolution  the  speed  of  the  driven  shaft,  therefore,  passes 


UNIVERSAL  AND  SLIP  JOINTS. 


167 


through  two  maxima  and  two  minima.  Its  average  speed,  of 
course,  is  the  same  as  that  of  the  driving  shaft,  and  the  speed 
fluctuation  amounts  to 


(1155-566)  X  100 
1,000 


=  28.9  per  cent. 


The  following  table  gives  the  speed  fluctuations  in  the  driven 
shaft  corresponding  to  different  angles  between  shafts,  the  speed 
of  the  driving  shaft  being  assumed  to  be  constant : 


Angle  & 

(Degrees.) 

2 

6 

8 
10 
12 
14 

I 


Fluctuation 
(Per  Cent.) 

0.15 

0.5 

1.1 

2. 

3. 

4.4 

6. 


Angle  <£ 
(Degrees.) 
16 
18 
20 
22 
24 
26 
28 


Fluctuation 
(Per  Cent.) 
7.9 

10. 

12.4 

15. 

18. 

21.3 

25. 


7200 
fjOO 
1000 
900 
fOO 

X 

.  — 

£ 

N 

/ 

X 

-Driven 
'Drtvint 

JM 

c    ^W? 

X 

\ 

x 

X 

' 

\ 

X 

—  •-' 

""K 

•—   _ 

JKofion  of  Driving  Shaft 
FIG.  108. — VARIATION  OF  DRIVEN  SHAFT  SPEED. 

(Angle  Between   Shafts,  30  Degrees.) 

This  fluctuation  in  the  speed  of  transmission  is  a  matter  of 
great  moment.  In  a  gasoline  automobile  we  have  at  one  end  of 
the  transmission  line  the  motor,  whose  speed  is  maintained  sub- 
stantially constant  by  a  heavy  flywheel,  and  at  the  other  end  the 
car,  which,  when  running  at  high  speed,  also  has  its  speed  main- 
tained by  inertia.  But  if  the  transmission  is  effected  through  a 
single  universal  joint  working  at  an  appreciable  angle,  the  speed 
of  either  the  car  or  the  engine,  or  of  both,  must  of  necessity 
change  greatly  in  a  quarter  revolution  of  the  driving  shaft.  The 
flywheel  inertia  strongly  resists  such  a  change  in  the  speed  of  the 
engine,  and  the  car  inertia  a  change  in  the  speed  of  the  car,  and 


168  UNIVERSAL  AND  SLIP  JOINTS 

the  result  is  that  every  part  of  the  transmission  line  is  subjected 
to  enormous  stresses.  Not  the  least  to  suffer  under  these  stresses 
are  the  tires,  which  tend  to  slip  on  the  ground  as  the  car  tends  to 
suddenly  accelerate.  To  minimize  these  stresses  the  drive  must  be 
so  arranged  that  the  two  shafts  are  always  nearly  in  line  with 
each  other.  They  can  be  entirely  eliminated  by  using  two  uni- 
versal joints  in  series.  We  found  that  the  speed  of  transmission 
is  reduced  in  a  certain  ratio  when  the  pin  of  the  driving  fork  is 
perpendicular  to  the  plane  through  the  shafts  and  increased  in  the 
inverse  proportion  when  the  pin  of  the  driving  shaft  is  in  the 
plane  of  the  shafts.  These  two  positions  are  90  degrees  apart. 
Hence,  by  arranging  two  universal  joints  in  series  (Fig.  109)  in 
such  relation  that  the  driving  fork  or  corresponding  member  of 


FIG.    109. — ANGUT.AR   RELATION   OF    DOUBLE    UNIVERSAL    JOINTS 
TO  INSURE  UNIFORM  TRANSMISSION  OF  MOTION. 

the  second  is  set  at  an  angle  of  90  degrees  with  respect  to  the  driv- 
ing fork  of  the  first,  and  so  that  the  driving  and  driven  shafts  are 
parallel,  both  making  the  same  angle  with  the  intermediate  shaft, 
then  motion  will  be  uniformly  transmitted  from  the  driving  to  the 
driven  shaft.  In  other  words,  the  pins  at  the  ends  of  the 
intermediate  shaft  must  be  in  the  same  plane,  or  parallel.  The 
intermediate  shaft,  of  course,  will  still  revolve  non-uniformly 
if  there  is  an  angle  between  it  and  either  of  the  shafts  con- 
nected by  it,  but  since  it  has  very  little  inertia  this  is  of  no 
importance. 

The  Square  Block  Type — The  square  block  type  of  joint 
can  hardly  be  recommended  for  such  important  work  as  in  the 
transmission  from  the  gear  box  to  the  rear  axle.  It  has  given  very 
good  satisfaction  in  individual  cases,  but  failed  absolutely  in  other 
cars  of  the  same  make.  It  must  be  remembered  that  in  this  type 
of  joint  there  is  a  line  contact  only,  and  the  bearing  pressures  are 


UNIVERSAL  AND  SLIP  JOINTS.  169 

necessarily  very  high.  Therefore,  if  lubrication  is  neglected  or  if 
the  bearing  surfaces  are  not  uniformly  hardened,  cutting  sets  in, 
and  once  there  is  a  little  play  the  joint  is  soon  hammered  out. 
This  type  of  joint  was  employed  in  the  1909  model  of  a  popular 
American  make  of  medium  priced  car,  but  was  discarded  the 
next  season.  For  a  four  cylinder  3%x4^  inch  engine  the  block 
measured  2x2  inches  and  was  ^  inch  wide. 

The  contact  surfaces  of  the  block  are  made  cylindrical.  If  the 
block  were  made  a  good  fit  in  the  sleeve  it  would,  of  course,  be 
possible  to  rock  it  in  one  or  the  other  of  two  planes,  but  not  in 
both  simultaneously.  However,  the  block  in  service  has  to  rock 
relatively  to  the  sleeve  in  every  direction,  and  to  make  this  possi- 
ble it  must  have  a  certain  amount  of  play  in  the  sleeve  when 
their  axes  are  parallel.  This  play,  of  course,  must  be  made  as 
small  as  possible,  because  it  is  a  source  of  noise  and  wear,  and 
it  will  naturally  increase  in  use.  The  problem  of  the  amount  of 
play  required  in  square,  pentagonal  and  hexagonal  block  joints 
to  allow  operation  at  certain  limiting  angles  has  been  investigated 
by  O.  Winkler  (Der  Motorwagen,  Nos.  3  and  4,  1912),  who 

D 
finds  that  the  ratio  —  of  the  diameter  of  the  block  and  that  of 

Dt 

the  recess  should  be  as  follows  for  various  limiting  angular  mo- 
tions. 

Limiting 

Angle  of 

Operation.  Ratios    of    Block    to    Recess    Diameters 

(Degrees.)  Square.  Pentagon.  Hexagon. 


.00031  1.00022  l.OOOi; 

.00122  1.00088  1.00062 

.00276  1.00198  1.00139 

.00490  1.00353  1.00247 

.00766  1.00551  1.00386 

.01102  1.00793  1.00555 

.01501  1.01080  1.00756 


16  1.01960  1.01411  1.00988 

18  1.02481  1.01785  1.01250 

20  1.03062  1.02204  1.01543 

Calculation  of  Forked  Types. — In  designing  the  forks  for 
universal  joints  comprising  such  members,  conflicting  require- 
ments are  met  with.  That  is,  if  the  fork  arms  are  spread  far  apart 
the  pressures  on  the  bearings  will  be  reduced  and  the  frictional 
loss  consequently  will  be  less,  but,  on  the  other  hand,  the  joint  has 
to  be  enclosed  and  forks  of  wide  spread  necessitate  a  bulky  and 
heavy  casing.  Usually  the  joint  is  made  as  compact  as  possible, 
and  the  bearings  are  made  large  enough  to  withstand  the  pres- 
sure. The  distance  between  the  middle  points  of  opposite  bearings 
is  usually  about  three  times  the  shaft  diameter.  This  distance, 
of  course,  is  a  matter  of  choice,  but  a  good  approximation  to 


170  UNIVERSAL  AND  SLIP  JOINTS. 

average  modern  practice  in  the  universal  joints  of  propeller  shafts 
is  obtained  by  making  it 

3 

d=  0.8  ^/T (42) 

where  T  is  the  normal  speed  torque  of  the  motor.  Of  course, 
the  greatest  torque  is  transmitted  by  the  propeller  shaft  uni- 
versals  when  the  low  gear  is  in  operation,  and  in  the  calculation 
of  the  parts  for  mechanical  strength  it  is  well  to  start  with  the 
maximum  torque  available  on  the  low  gear.  On  the  other  hand, 
in  determining  the  bearing  surfaces  the  pressures  on  direct  drive 
should  be  figured  with,  as  in  most  cars  the  direct  drive  is  used 
a  very  large  proportion  of  the  time;  and,  besides,  the  rubbing 
speed  at  the  bearing  surfaces  of  the  universal  is  far  greater  when 
the  direct  drive  is  in  operation  than  when  the  power  is  trans- 
mitted through  the  low  gear.  The  bearings  of  universal  joints  of 
the  types  shown  in  Figs.  102-105  are  so  proportioned  that  the  unit 
bearing  pressure  at  full  engine  load  on  direct  drive  is  500  pounds 
per  square  inch.  The  length  and  diameter  of  the  bearings  usually 
bear  to  each  other  the  ratio  of  4  to  3. 

We  will  now  illustrate  the  calculation  of  a  universal  joint  by  a 
practical  example.  The  joint,  we  will  suppose,  is  to  transmit  the 
powtr  of  a  four  cylinder  4x5  inch  motor  (normal  speed  torque  = 
108  lbs.-ft.),  and  the  low  gear  ratio  is  3.2. 

The  distance  between  the  middle  points  of  the  bearings  would  be 

o .  8  I/ ^s  =  3  •  8 1  —  say  3!  inches. 

This  gives  a  mean  bearing  radius  of  1%  inches  and  makes  the 
bearing  pressure  for  the  direct  drive 

Io8*12  ^691  pounds. 

This  pressure  being  taken  up  on  two  bearings,  the  pressure  on 
each  is  345-5  pounds,  and  at  500  pounds  per  square  inch  the  pro- 
jected area  of  each  must  be 

345 -5  —  o>6g!  SqUare  inch. 

500 

If  the  length  of  the  bearing  is  to  be  4/3  the  diameter,  then  the 
projected  area  is  4/3  d2  and 

JL,  d2  =  0.691  square  inch. 
3 

c£2  =  Ji-X  0.691  =0.518  square  inch 
4 

and 

d  =  N/o.i8  =0.72  —  say,  f  inch. 


UNIVERSAL  AND   SLIP  JOINTS. 


171 


The  length  is 

4 

—  X  0.72  =  0.96  —  say,  1  inch. 

o 

It  is  to  be  remembered  that  if  the  bearings  are  spaced  farther 
apart  their  dimensions  can  be  made  smaller. 

The  low  speed  or  maximum  torque  of  our  motor  is  133 
pounds- feet,  and  the  torque  to  be  figured  on  in  calculating  parts 
for  strength  is 

3.2  X  133  =  425.6  pounds-feet. 

If  the  universal  joint  is  to  be  secured  to  the  shaft  with  a  key  its 
hub  is  generally  made  with  a  diameter  of  1.6  the  shaft  diameter, 
and  its  length  is  made  about  the  same  as  its  outside  diameter. 

4- 


FIG.  110. — DETERMINATION  OF  STRESS  IN  FORK  ARM. 

Assuming  the  propeller  shaft  to  be  of  \y^  inches  diameter,  the 
hub  diameter  and  length  should  be 

1.6  X  1.25  =  2  inches. 

We  now  have  the  sizes  of  the  hub  and  the  bearings  and  their 
relative  positions.    We  lay  these  down  on  the  drawing  board  and 
sketch  in  the  arms,  as  shown  in  Fig.  110.    When  the  car  is  run- 
ning under  full  power  on  the  low  gear  there  is  a  normal  force  of 
425  X  12  =  ^Qpounds 

2X  if 

acting  at  point  a.  Now,  we  take  any  section  of  the  arm  like  A  A 
and  draw  a  perpendicular  cb  to  the  middle  point  of  this  section. 
Next  we  construct  a  right-angled  triangle  with  cb  as  the  base  and 
a  as  the  apex.  Evidently  the  force  of  1,360  Ibs.,  acting  normally  to 
the  paper  at  a  produces  in  the  section  AA  of  the  arm  a  torsional 


172  UNIVERSAL  AND  SLIP  JOINTS. 

stress  proportional  to  the  arm  ab  (which  by  measurement  is  found 
to  be  %  inch),  and  a  bending  stress  proportional  to  arm  cb 
(which  is  found  to  be  1^4  inches).  Hence  the  torsional  moment  is 

Aft  =  H   X   1360  =  850  pounds-inches. 
and  the  bending  moment, 

Mb  =  \Y4  X  1360  =  1700  pounds-inches. 

As  drawn  in  Fig.  110,  the  section  of  the  arm  at  A  A  is  equiva- 
lent to  a  rectangle  measuring  l/2  inch  x  1^4  inches.  The  proper 
method  of  procedure  is  to  assume  a  section  like  this,  and  then 
calculate  the  stress  in  the  arm  under  the  combined  bending  and 
torsional  moments,  and  if  it  figures  out  either  too  high  or  too 
low  to  change  the  section  accordingly. 

We  first  find  the  stress  due  to  the  bending  moment,  and  that 
due  to  the  torsional  moment  separately,  and  then  combine  the 
two.  The  bending  stress  is  found  by  means  of  the  equation 

Me 

Ob  j 

where  M  is  the  bending  moment,  c  the  distance  of  the  outermost 
fibre  from  the  neutral  axis,  and  /  the  moment  of  inertia  of  the 
section  around  the  neutral  axis  for  bending  stresses.  M  in  our 
case  is  1700  pounds-inches;  c,  fy&  inch,  and  / 


=   0.0814 


12 

Hence  the  bending  stress  is 
1,700  X  0.625 
-  .  -  =  13,050  pounds  per  square  inch. 

0.0814 

The  formula  for  the  shearing  stress  due  to  the  torsion  is  ex- 
actly the  same  as  that  for  the  bending  stress,  but  /  in  this  case 
represents  the  polar  moment  of  inertia  of  the  section,  and  M  and 
c,  of  course,  have  different  values. 

M  =  850  pounds-inches. 

=  0.673 


y2  x  iy45       iy4  x  y2* 

+  -  =  0.0944. 


12  12 

Hence*  the  stress  due  to  torsion  is 

850  «X  0.673 
-  =  6,060  pounds  per  square  inch. 

0.0944 
Calling  the  bending  stress  S\>  and  the  torsional  stress  St,  the 

total  stress  in  the  material  is 

y2  sb  +  \ss  +  y4ss 

(Merriman,   Mechanics   of   Materials,  •  Fourth   Edition,   p.    152). 


UNIVERSAL  AND  SLIP  JOINTS.  173 

Hence -in  this  case  the  combined  stress  is 


-f-  <4/6,o6o2  -I-  I3>°5°2  =  15,430  pounds  per  square  inch. 


13-050 

2 

which  is  reasonable,  though  somewhat  higher  than  the  stress  in 
the  shaft.  If  it  is  thought  desirable,  a  similar  calculation  can  be 
carried  through  for  another  section  of  the  arm,  but  usually  a 
single  calculation  would  .be  considered  sufficient,  the  arm  being 
tapered  slightly  from  end  to  end.  The  forks  are  generally  drop 
forged  and  occasionally  ca^st,  and  the  section  must  be  given  the 
necessary  draft  of  about  8  degrees.  The  thickness  of  the  walls 
of  the  bearing  hubs  and  the  cross  can  be  made 

—  4- -I  inch,  where  d  is  the  diameter  of  the  pin. 
4       16 

This  makes  the  bearing  diameter  larger  than  the  cross  diameter 
by  twice  the  thickness  of  the  bushing.  For  the  sake  of  appear- 
ance it  is  well  to  have  the  two  diameters  approach  each  other 
gradually  at  the  junction,  and  this  can  be  accomplished  by  either 
making  the  bearing  hub  barrel  shaped,  as  shown,  or  else  provid- 
ing the  cross  with  circumferential  flanges  at  the  ends  of  its  arms. 
These  flanges  strengthen  it  considerably  and  permit  of  reducing 
the  thickness  of  the  metal  between  them. 

Calculation  of  Block  and  Trunnion  Type — In  this  type  of 
universal  joint  the  bore  of  the  shell  is  made  sufficiently  large 
to  allow  the  shaft  the  necessary  freedom  of  angular  motion, 
and,  therefore,  can  be  best  determined  on  the  drawing  board. 
The  pins  are  so  proportioned  that  the  unit  pressure  on  them 
when  the  engine  is  driving  direct  at  normal  speed  under  full 
power,  figures  out  to  about  1,000  pounds  per  square  inch.  The 
unit  pressure  between  the  blocks  and  the  walls  of  the  slot 
can  be  made  between  600  and  700  pounds  per  square  inch.  The 
trunnions  are  generally  made  of  about  the  same  length  as  their 
diameter.  As  a  precaution,  the  stress  at  the  bottom  section  of 
the  pin  corresponding  to  maximum  engine  torque  and  low  gear 
operation,  should  be  calculated.  All  of  the  bearing  parts  of  a 
joint  of  this  type  should  be  hardened  or  case  hardened  and 
ground.  It  is  the  hardened  steel  bearing  surfaces  that  make 
possible  the  greater  unit  bearing  pressures  as  compared  with 
other  types  of  universal  joints.  The  length  of  the  slots  will 
depend  somewhat  on  the  spring  action  and  on  the  length  and 
inclination  of  the  shafts  to  be  connected.  It  is  generally  about 
equal  to  the  outside  diameter  of  the  shell. 

This  type  of  joint  is  very  largely  used  at  the  rear  end  of  a 
propeller  shaft  provided  with  two  universal  joints,  serving  both 


174  UNIVERSAL  AND  SLIP  JOINTS. 

as  a  universal  and  slip  joint.  Occasionally  two  of  these  joints 
are  used  in  a  single  shaft,  in  which  case  it  is  necessary  to  hold 
the  ball  of  one  joint  between  stops  or  to  centre  the  shaft  be- 
tween springs,  as  illustrated  in  Fig.  105.  Neglect  of  this  pre- 
caution will  not  only  result  in  noisy  operation,  but  will  make 
it  difficult  to  keep  the  lubricant  in  the  joint  housing.  The  slid- 
ing blocks  should  preferably  be  cut  with  slanting  oil  grooves 
across  their  bearing  surfaces  to  insure  effective  lubrication. 

Lubrication  and  Dust  Protection— On  the  earlier  shaft 
d-riven  cars  the  universal  joints  were  not  enclosed  and  k  was 
found  very  difficult  to  lubricate  them  effectively.  Centrifugal 
force  would  cause  the  joint  to  throw  the  oil  off  and  grit  would 
work  into  the  bearings  and  cause  their  rapid  destruction.  This 


FIG.   in. — LEATHER  BOOT  FOR  UNIVERSAL  JOINT. 

was  remedied  to  an  extent  by  making  the  bearing  bushings 
thimble  shaped,  that  is,  "blind"  at  their  outer  end,  but  the  most 
effective  remedy  undoubtedly  consists  in  enclosing  the  whole 
joint  oil  and  dust  proof.  There  are  various  methods  of  accom- 
plishing this. 

The  universal  joint  which  is  easiest  to  enclose  is  the  block 
and  trunnion  type.  As  shown  in  Fig.  in,  it  is  provided  with  a 
tight  fitting  tubular  steel  housing  over  the  part  which  we  have 
called  the  shell,  fitted  against  a  shoulder  turned  thereon  and 
secured  in  position  by  means  of  a  couple  of  machine  screws. 
This  housing  can  have  a  groove  formed  on  it  at  its  open  end 
to  which  a  leather  boot  can  be  fastened  whose  other  end  is 
tied  around  the  shaft.  It  is  a  good  plan  to  rivet  a  fitting, 


UNIVERSAL  AND  SLIP  JOINTS. 


175 


closed  by  a  quarter  inch  pipe  plug,  to  the  leather  boot,  for 
convenience  in  replenishing  the  lubricant.  The  leather  boot  is 
fastened  in  place  by  means  of  clamps,  similar  to  hose  clamps. 
If  one  end  is  clamped  tight  to  the  shaft,  sufficient  slack  must 
be  allowed  in  the  boot  to  permit  the  shaft  to  swing  freely  in 
all  directions  through  its  maximum  operating  angle.  Some 
makers  clamp  the  small  end  of  the  boots  to  a  sliding  sleeve 
on  the  shaft,  enabling  the  boot  to  readily  accommodate  itself 
to  varying  angularities  between  the  two  shafts. 

Another  form  of  universal  joint  housing  is  illustrated  in  Fig. 
112.    One  member  of  the  joint  is  made  in  the  form  of  a  plate  to 


FIG.  ii2.— SHEET  METAL  HOUSING. 

which  is  bolted  a  spun  sheet  metal  housing  which  is  partly 
cylindrical  and  partly  spherical.  Against  the  spherical  portion 
of  this  housing  bears  another  sheet  metal  part  in  the  form 
of  a  spherical  zone,  the  latter  being  secured  to  the  hub  of  the 
universal  joint  fork.  This  type  of  housing  is  applicable  only 
to  joints  whose  two  axes  intersect,  and  the  centre  of  the  spher- 
ical portions  must  be  at  the  point  of  intersection  of  these  two 
axes.  The  cover  plate  is  formed  with  a  groove  near  its  edge 
which  is  filled  with  packing  material. 

Fig.  113  shows  still  another  form  of  housing.  It  is  sub- 
stantially ball  shaped  and  consists  of  three  parts.  Two  of 
these  are  bolted  together  and  form,  between  them,  bearings  for 
two  of  the  trunnions  of  a  cross,  one  of  these  two  parts  being 
keyed  to  one  of  the  connected  shafts.  The  arms  of  the  cross 


176 


UNIVERSAL  AND  SLIP  JOINTS. 


are  of  unequal  length,  the  two  longer  arms  having  bearings  in  the 
housing,  and  the  two  shorter  ones  in  the  ends  of  the  arms  of  a 
fork  secured  to  the  other  shaft.  The  latter  shaft  extends  through 
a  circular  opening  in  the  ball  shaped  housing,  sufficiently  larger 
than  the  shaft  to  permit  of  its  swinging  to  the  maximum  angle 
of  operation  in  any  direction.  This  opening  is  closed  by  a  zone 
shaped  cover  which  is  pressed  against  a  machined  surface  on  the 
inside  of  the  housing  by  a  coiled  spring. 

Where  a  single  universal  joint  is  used  in  the  propeller  shaft 
and  the  latter  is  surrounded  by  a  torque  tube,  the  forward  end 
of  this  torque  tube  is  often  supported  by  a  ball  and  socket 


FIG.  113. — ENCLOSED  UNIVERSAL  JOINT. 

joint,  secured  to  a  cross   frame  member,  the  ball  being  made 
hollow  and  serving  as  a  housing  for  the  universal. 

Anti-Friction  Bearing  Universals. — Anti-friction  bearings 
have  been  used  in  universal  joints  to  a  small  extent.  Fig.  114 
shows  the  Lancia  joint  which  is  fitted  with  radial  ball  bearings. 
It  is  of  the  fork  and  internal  ring  type.  The  use  of  ball  bear- 
ings has  led  to  a  special  method  of  assembling.  It  will  be 
seen  that  the  fork  ends  are  slotted,  the  slots  being  just  large 
enough  to  permit  of  the  trunnions  being  passed  through  them- 
The  ball  bearings  are  then  slipped  over  the  trunnions  and  into 
their  seats  in  the  fork  ends  and  the  outer  races  are  secured  in 
place  by  means  of  cap  plates.  The  H.  H.  Franklin  Mfg.  Co. 
uses  rollers  in  the  blocks  of  a  block  and  trunnion  type  of  uni- 
versal joint.  These  entirely  fill  the  space  between  block  and 


UNIVERSAL  AND  SLIP  JOINTS. 


177 


trunnion,  and  are  held  in  place  by  end  washers,  no  cages  being 
used. 

It  is  hardly  to  be  expected  that  much  saving  in  power  will 
result  from  the  use  of  anti-friction  bearings  at  this  point,  be- 
cause of  the  small  angularity  of  the  shafts  and  the  consequent 
limited  motion  at  the  joint  bearings  in  modern  cars.  Probably 
the  chief  advantage  of  such  bearings  in  this  place  is  that  they 
are  not  so  easily  damaged  as  plain  bearings  if  the  lubrication 
should  be  neglected. 

Slip  Joints. — Unless  a  combined  universal  and  slip  joint  like 
the  square  block  type  or  the  block  and  trunnion  type  is  used 


t  FIG.  114.— LANCIA  BALL  BEARING  UNIVERSAL  JOINT. 

in  the  propeller  shaft,  a  special  slip  joint  must  be  provided 
to  allow  for  variations  in  the  distance  between  the  change  gear 
box  and  the  rear  axle  housing,  due  to  play  of  the  springs.  This 
may  be  either  a  squared  or  a  fluted  shaft  with  a  corresponding 
hub  or  sleeve.  It  -may  be  stated  at  once  that  the  block  and 
trunnion  type  of  joint  is  far  preferable,  since  the  sliding  motion 
occurs  farther  away  from  the  axis  of  rotation,  hence  the  pres- 
sure on  the  sliding  surface,  and  consequently  the  resistance  to 
sliding,  is  much  smaller.  Fig.  114  illustrates  a  four  fluted  sliding 
joint.  Six  fluted  shafts  are  also  used.  The  Society  of  Automo- 
bile Engineers  has  standardized  fluted  shafts  and  given  rules  for 
their  load  capacity  (see  Appendix). 

Leather    Disc    Universal    Joints. — Leather    universal    joints 
have     been     used     chiefly    between     the     clutch     and     change 


178 


UNIVERSAL  AND  SLIP  JOINTS. 


speed  gear.  These  universals  are  silent  in  operation  and  they 
are  not  subject  to  bearing  friction,  consequently  they  are  highly 
efficient  as  regards  the  transmission  of  power.  A  leather  uni- 
versal joint  consists  of  two  similar  spiders,  usually  three-armed, 
fastened  to  the  ends  of  the  shafts  to  be  connected  and  of  a 
number  of  leather  discs  or  rings  bolted  between  the  spiders. 
The  arms  of  the  two  spiders  are  staggered,  so  that  any  arm 
of  one  of  the  spiders  is  located  midway  between  two  arms  of 
the  other  spider.  Three,  four  or  five  discs  may  be  used  and 
individual  discs  are  often  spaced  by  steel  washers.  It  will  at 
once  be  seen  that  the  ability  of  such  a  universal  to  transmit 
motion  between  shafts  at  an  angle  is  limited  as  to  the  angle. 


FIG.  115. — TYPICAL  DESIGN  OF  LEATHER  Disc  UNIVERSAL  JOINT. 

A  typical  leather  universal  is  illustrated  in  Fig.  115.  This 
shows  four  leather  discs  between  the  two  spiders,  each  pair  of 
discs  separated  by  steel  washers  at  the  points  where  the  bolts 
pass  through.  These  steel  washers  distribute  the  driving  strain 
over  a  larger  area  and  also  increase  the  flexibility  or  freedom 
of  action  of  the  joint. 

It  is  impossible  to  calculate  the  actual  stress  in  the  leather 
when  the  joint  works  at  an  angle.  It  increases,  of  course,  rap- 
idly with  the  angle.  For  insertion  between  the  clutch  and 
chpnge  gear,  where  very  little  universal  action  is  called  for,  a 
stress  in  the  leather  of  200  Ibs.  per  square  inch  may  be  allowed. 
Thus,  let  T  be  the  maximum  torque  of  the  engine;  n,  the  num- 
ber of  discs;  do,  the  outside  diameter;  di,  the  inside  diameter, 


UNIVERSAL  AND  SLIP  JOINTS.       .  179 

and  t,  the  thickness  of  the  leather.  Then  with  three-armed 
spiders  the  load  is  divided  between  3  n  sections  of  the  leather 
with  a  combined  cross-sectional  area  of  3  nt  square  inch.  The 
tangential  force  is 

2  T  X  12 
p  =  

do   +   di, 

which  may  be  solved  for  do  after  first  assuming  a  certain  rela- 
tion between  do  and  di. 


FIG.  116. — LEATHER  DOUBLE  UNIVERSAL  JOINT   (OVERLAND). 

Experience  with  leather  universal  joints  has  not  been  uni- 
formly successful  and  the  greatest  care  is  required  in  their 
design.  The  bosses  of  the  spider  arms  where  they  bear  against 
the  leather,  and  the  washers  must  be  carefully  rounded,  and 
only  the  best  grade  of  chrome  leather  must  be  used.  Some 
manufacturers  are  said  to  treat  the  leather  with  linseed  oil  to 
make  it  more  flexible  and  proof  against,  the  effects  of  moisture. 
If  there  is  too  much  end  strain  on  the  universals  the  leather 
discs  will  "cup"  and  pull  apart.  One  scheme  to  prevent  this 
consists  in  inserting  two  or  three  thin  sheet  steel  rings  between 
adjacent  leather  rings  and  riveting  the  whole  together. 

Rubberized  fabric  discs  are  sometimes  used  in  place  of  the 
leather.  TLe  discs  are  built  up  of  layers  of  fabric  with  the 
warp  of  succeeding  layers  at  slightly  different  angles.  In  fact 
the  whole  circle  is  divided  into  a  number  of  parts  equal  to  the 
number  of  layers  in  the  discs  and  the  angle  thus  arrived  at  is 
the  angle  between  the  warp  of  adjacent  discs. 


CHAPTER  VII. 


THE  DIFFERENTIAL   GEAR. 

The  purpose  of  the  differential  gear,  as  explained  in  Chapter  1, 
is  to  permit  of  equally  dividing  the  driving  effort  of  a  single 
source  of  motive  power  between  two  driving  wheels  and  to  allow 
cars  driven  through  wheels  on  opposite  sides  to  be  freely  steered. 
There  are  two  general  types  of  differential  gears,  viz.,  the  bevel 
type  and  the  spur  type. 

A  bevel  type  differential  gear  consists  of  two  bevel  gears  ar- 
ranged coaxially  and  facing  each  other,  and  a  varying  number 
of  bevel  pinions  between  them  meshing  with  both  of  the  gears. 
Generally  either  three  or  four  pinions  are  used,  which  are  placed 
at/ equal  angular  distances.  The  pinions  are  capable  of  rotating 
on  radial  studs  which  are  clamped  at  their  outer  ends  between 
the  two  halves  of  a  housing  or  skeleton  frame.  This  frame  is 
provided  with  hubs  carried  in  ball  or  roller  bearings  in  the  rear 
axle  or  jackshaft  housing  and  with  a  flange  to  which  the  driven 
bevel  gear,  sprocket,  etc.,  can  be  secured. 

Action  of  the  Differential— Power  is  thus  applied  to  the 
frame  or  housing  of  the  differential.  The  housing  transmits  it  to 
the  bevel  pinions,  the  latter  to  the  bevel  gears  and  these  to  the 
rear  axle  shafts  or  jackshafts.  Under  any  given  conditions  of 
operation  a  certain  torque  is  impressed  upon  the  differential 
housing.  This  torque  is  divided  equally  between  the  three  or 
four  bevel  pinions.  Each  bevel  pinion  constitutes  a  balance  lever 
between  the  two  bevel  gears  and  evenly  divides  its  torque  be- 
tween them.  Thus  the  total  torque  impressed  upon  the  differ- 
ential housing  is  at  all  times  equally  divided  between  the  two 
bevel  gears,  also  called  the  master  gears. 

The  relative  motion  of  the  two  side  gears  depends  upon  the 
position  of  the  steering  gear  and  upon  the  traction  conditions. 
Suppose  first  that  both  driving  wheels  run  on  dry  road  surface 
sc  there  is  plenty  of  road  adherence.  Then  the  rate  of  revolu- 

180 


THE  DIFFERENTIAL  GEAR.  181 

tion  of  each  wheel  and  that  of  the  corresponding  master  gear  of 
the  differential  will  depend  upon  the  length  of  the  path  followed 
by  that  wheel.  If  the  steering  road  wheels  are  in  the  straight- 
ahead  position  and  both  driving  wheels  have  exactly  the  same 
diameter,  then  both  will  rotate  at  the  same  speed,  as  will  the 
differential  master  gears.  On  the  other  hand,  if  the  steering  road 
wheels  are  deflected  from  the  straight-ahead  position  the  vehicle 
is  constrained  to  travel  in  a  curve,  and  the  wheels  on  the  outside 
of  the  curve  will  be  forced  to  turn  faster  than  those  on  the 
inside.  Under  these  conditions  the  pinions  of  the  differential  will 
turn  on  their  studs,  allowing  one  master  gear  to  run  faster  than 
the  other.  The  speed  of  the  frame  or  housing  of  the  differential 
is  always  equal  to  the  algebraic  mean  of  the  speeds  of  the  two 
master  gears. 

In  case  one  of  the  wheels  stands  on  slippery  ground  and  has 
insufficient  road  adherence,  it  will  slip.  The  differential  gear 
under  these  conditions  also  divides  the  propelling  effort  equally 
between  the  two  driving  wheels,  and  the  wheel  which  stands  on 
dry  surface  can  exert  no  more  propelling  effort  than  the  one  on 
slippery  surface.  The  car  will  thus  be  stalled,  and  the  wheel  on 
slippery  ground  will  be  spun  around  at  twice  the  rate  at  which 
it  would  otherwise  turn  with  the  engine  running  at  the  same 
speed,  whereas  the  other  wheel  will  remain  stationary.  This 
quality  may  be  regarded  as  a  defect  of  the  differential  gear,  espe- 
cially in  the  case  of  very  heavy  vehicles,  and  such  vehicles  are 
often  provided  with  a  differential  lock,  consisting  of  some  means 
for  so  connecting  the  two  master  gears  of  the  differential  to- 
gether that  they  must  rotate  in  unison. 

Calculation  of  Bevel  Type  Differential. — Differential  gears 
are  made  very  compact,  being  almost  a  solid  box  of  gears.  In 
calculating  their  dimensions  it  is  advisable  to  base  the  calculation 
upon  the  maximum  torque  on  the  rear  axle  under  low  gear,  for 
the  reason  that  the  pinions  and  gears  operate  only  occasionally 
and  then  only  for  short  periods  at  a  time.  They  are,  however, 
constantly  subjected  to  the  stress  due  to  the  torque  being  trans- 
mitted through  their  teeth. 

The  torque-transmitting  capacity  of  a  bevel  type  differential 
gear  varies  as  the  square  of  the  largest  pitch  diameter  of  the 
master  gears,  because  the  lever  arm  through  which  the  tooth 
pressure  acts  is  proportional  to  this  pitch  diameter  and  the  face 
width  of  the  tooth,  and  hence  the  permissible  tooth  pressure,  also 
varies  with  the  largest  pitch  diameter.  It  also  varies  as  the  cir- 
cular pitch  of  the  teeth  and  as  the  number  of  bevel  pinions  em- 


182 


THE  DIFFERENTIAL  GEAR. 


ployed.  Of  course,  the  strength  of  the  material  also  has  an  in- 
fluence on  the  capacity  of  the  differential,  but  inasmuch  as 
low  carbon  steels  are  used  in  almost  every  instance,  the  tensile 
strengths  of  which  do  not  vary  much,  we  may  neglect  it.  A  con- 
siderable amount  of  practical  data  from  modern  cars  shows  that 
the  largest  pitch  diameter  of  the  master  gears  may  be  determined 
by  means  of  the  equation 

pdm  = 

70  pn 

where  T  is  the  maximum  low  gear  torque  on  the  rear  axle,  p 
the  circular  pitch  of  the  teeth  and  n  the  number  of  pinions. 


FIG.  117. — LONGITUDINAL  SECTION   THROUGH   BEVEL  TYPE 
DIFFERENTIAL  GEAR. 

The  numbers  of  teeth  generally  range  between  28  and  36  for 
the  master  gears  and  16  and  20  for  the  pinions,  the  gears  having 
about  1.8  times  the  number  of  teeth  as  the  pinions.  The  maxi- 
mum pitch  diameter  of  the  master  gear  having  been  determined, 
the  pitch  is  chosen  to  give  a  number  of  teeth  within  the  range 
mentioned.  Gears  of  8  pitch  are  generally  used  for  small  and 
moderate  powers  and  6  pitch  for  high  powers.  The  face  of  the 
gears  is  made  from  ^  to  ^  the  distance  from  the  intersection  of 


THE  DIFFERENTIAL  GEAR. 


183 


the  two  maximum  pitch  diameters  to  the  centre  of  the  differential. 
The  unit  pressure  on  the  pinion  pins  is  calculated  on  the  basis  of 
4,500  pounds  per  square  inch  under  maximum  engine  torque  and 
low  gear,  and  the  pin  diameter  is  generally  made  equal  to  three- 
fourths  the  bearing  length. 

After  the  dimensions  of  the  differential  have  been  roughly  de- 
termined by  means  of  the  above  rules,  a  layout  can  be  made 
and  the  design  checked  up  by  calculating  the  stress  in  the  teeth 
of  the  bevel  pinion,  which  should  be  in  the  neighborhood  of 
45,000  pounds  per  square  inch.  We  will  carry  these  calculations 


FIG.  118.— BEVEL  DIFFERENTIAL  PARTLY  IN  SECTION. 

through  for  a  rear  axle  differential  for  a  car  with  four  cylinder 
4x5  inch  motor,  a  low  gear  reduction  of  3.2  and  a  bevel  gear  ratio 
of  3.5.  The  maximum  rear  axle  torque  therefore  is 

3.2  X  3.5  X  133  =  1,490  pounds-feet. 

Let  the  differential  be  made  with  four  pinions  of  8  pitch;  then, 
according  to  equation  (43)  the  maximum  pitch  diameter  of  the 
master  gears  should  be  approximately 


1,490 


=  3.65  inch, 


70  X  0.4  X  4 

and  the  number  of  teeth  figures  out  to  29.    However  the  number 


184  THE  DIFFERENTIAL  GEAR. 

of  teeth  must  be  divisible  by  4,  there  being  four  pinions.  Hence 
we  will  choose  28  teeth.  The  pinions  then  should  have 

28 

—  =  16  teeth 

1.8 

and  their  maximum  pitch  diameter  will  be  2  inches.  The  distance 
of  the  intersection  of  the  two  largest  pitch  diameters  from  the 
centre  of  the  differential  is 


4 


3.52  +  22 

=  1.88  inches, 


4 
hence  the  face  of  the  gears  can  be  made 

0.35  X  1.88  =  0.66  —  say,  11/16  inch. 
Since  we  are  making  the  face  of  the  pinion  equal  to 
0.68  X   100 

=  36 

1.88 

per  cent,  of  the  distance  from  the  point  of  intersection  of  the 
largest  pitch  diameters  to  the  vertex  of  the  cone,  and  since  the 
strength  of  the  tooth  section  varies  uniformly  from  the  outer  to 
the  inner  end  of  the  tooth  in  proportion  to  the  distance  from  the 
centre  of  the  differential,  the  load  on  the  tooth  may  be  considered 
to  be  concentrated  on  the  pitch  line  at 

P        /100  +  64  \ 

\IIOQP  — I  -     X  36  1=  84  per  cent.* 

of  the  distance  between  the  outer  end  of  the  tooth  and  the  apex 
of  the  cone,  from  the  apex.  Hence  the  arm  through  which 
this  pressure  acts  is 

3.5  X  84 

=   1.47  inches, 

2  X   100 

and  the  tangential  pressure  on  the  mean  pitch  circle  is 
1,490  X  12 

=  12,150  pounds. 

1.47 

In  Fig.  119  is  shown  a  portion  of  the  top  view  of  an  18  tooth 
bevel  pinion  meshing  with  a  32  tooth  bevel  gear.  Gear  and  pin- 
ion are  shown  meshed  in  three  relative  positions,  and  it  will  be 
seen  that  in  each  position  there  are  two  or  more  teeth  of  the 
pinion  in  contact  with  teeth  of  the  gear.  Hence  we  can  figure 
that  the  load  is  taken  up  on  two  teeth  at  each  meshing  point,  and 
since  there  are  eight  meshing  points  in  a  four  pinion  differential, 
the  total  load  is  taken  up  on  16  teeth,  which  makes  the  load  per 
tooth  12>15Q 

=  760  pounds. 

16 
*  For  an  explanation  of  the  method  employed  see  page  225. 


THE  DIFFERENTIAL  GEAR. 


185 


The  strength  of  bevel  gear  teeth  can  be  calculated  by  a  method 
similar  to  that  of  Lewis  for  spur  teeth.  The  largest  section  of  a 
bevel  gear  tooth  has  the  same  strength  as  a  tooth  of  a  spur  gear 
of  the  same  pitch  and  number  of  teeth,  and  the  strength  of  the 
bevel  tooth  decreases  uniformly  as  the  apex  of  the  cone  is  ap- 
proached. Since  the  tooth  in  the  present  case  extends  36  per 
cent,  of  the  distance  from  the  base  to  the  apex  of  the  cone,  the 
average  strength  of  the  tooth  will  be  about  26  per  cent,  less  th<an 


FIG.  119.— EIGHTEEN  TOOTH  BEVEL  PINION  AND  THIRTY-TWO  TOOTH 

BEVEL  GEAR  IN  DIFFERENT  POSITIONS  OF  MESH,  SHOWING  THAT 

THE  PRESSURE  Is  ALWAYS  DIVIDED  BETWEEN  AT  LEAST 

Two  TEETH. 


that  of  a  corresponding  spur  tooth.     Substituting  in  the  Lewis 
formula  the  values  applying  to  our  case,  we  have 

760  =  5  X  0.4  X  11/16  X  0.083  X  0.74, 
and 

760 

•S* r  =  45,000  pounds  per  square  inch. 

0.4  X  11/16  X  0.083  X  74 
This  tooth  stress  is  in  harmony  with  the   stresses  allowed  in 


186  THE  DIFFERENTIAL  GEAR. 

» 

change  gear  pinions  as  given  in  the  chapter  on  sliding  change 
gears,  remembering  that  the  differential  pinions  and  gears  run 
together  little.  In  reality  the  stress  is  lower  because  the  Lewis 
formula  is  based  on  the  assumption  that  the  whole  tangential 
force  comes  on  the  end  of  the  tooth,  and  it  is  obvious  that  when 
two  or  more  teeth  of  one  gear  are  in  contact  with  teeth  of  the 
other  at  the  same  time,  at  least  one  tooth  takes  its  pressure  at  a 
point  considerably  nearer  its  root,  whereby  the  moment  of  the 
pressure  is  reduced. 

The  pressure  on  each  pinion  pin  is 
12,150 

=  3,040  pounds 

4 

and  with  a  unit  bearing  pressure  of  4,700  pounds  per  square  inch 
the  required  bearing  surface  figures  out  to 
3,040 

=  0.675  square  inch. 

4,700 

Since  the  bearing  length  is  to  be  to  the  diameter  as  4  to  3,  the 
area  will  be  4 

—  d2  =  0.675  square  inch. 
3 
Hence 

d2  =  Y4  X  0.675  =  0.506  square  inch, 
and 

d  ="\/0.506  =  0.71  inch— say,  11/16  inch, 
whereas  the  length  should  be 
4        11 

_  X  —  =  0.916— say,  15/16  inch. 
3         16 

The  pinion  pins  are  generally  made  integral  with  a  central 
ring  having  a  bearing  on  the  hubs  of  the  master  gears,  thus 
forming  a  spider.  Their  outer  ends  may  be  clamped  between  the 
halves  of  the  frame  or  housing,  or  they  may  be  flattened  off 
and  the  holes  for  them  made  rectangular,  with  their  long  sides 
parallel  with  the  axis  of  the  differential  so  the  spider  may  slide 
in  these  holes  and  automatically  adjust  itself  to  the  position 
where  the  pinions  mesh  equally  with  both  master  gears.  The  hubs 
of  the  master  gears  are  generally  broached  out  square  to  fit  to 
the  squared  ends  of  the  rear  axle  shafts.  These  hubs  are  pro- 
vided with  a  radial  face  which  bears  against  a  corresponding  face 
on  the  outside  of  the  housing  to  take  up  the  bevel  gear  end 
thrust.  Some  designers  provide  bronze  bearing  bushings  and 
thrust  washers,  but  the  majority  do  not.  The  flange  for  the 
driven  bevel  gear  is  formed  integral  with  one-half  of  the 


THE  DIFFERENTIAL  GEAR.  187 

differential  housing,  and  is  often  so  far  offset  to  one  side  as 
to  bring  the  centre  of  the  differential  in  line  with  the  driving 
pinion  centre. 

The  Spur  Differential— Referring  to  Figs.  120  and  121  a 
spur  differential  consists  of  two  spur  master  gears  mounted  on 
the  inner  ends  of  the  differential  shafts,  of  a  varying  number 
of  pairs  of  spur  pinions  and  of  a  housing  or  frame  surrounding 
the  whole.  The  spur  pinions  are  of  substantially  double  the  width 
of  the  spur  gears;  the  latter  are  placed  some  distance  apart 
and  the  extra  width  of  the  pinions  extends  into  this  inter- 
mediate space  where  the  two  pinions  of  each  pair  mesh  together, 


FIG.  120. — LONGITUDINAL  ELEVATION  OF  SPUR  DIFFERENTIAL,  HALF 
SECTIONED. 

The  action  of  this  type  of  differential  is  exactly  the  same  as 
that  of  a  bevel  differential. 

The  pinions  of  spur  gear  differentials  are  made  with  a  very 
small  number  of  teeth,  generally  about  ten,  because  any  small 
increase  in  their  size  entails  a  large  increase  in  the  bulk  of  the 
differential  housing.  Stub  teeth  are  preferably  used,  and  some 
makers  use  a  special  form  of  mongrel  teeth  of  still  greater 
strength  than  stub  teeth. 


158 


THE  DIFFERENTIAL  GEAR. 


Spur  differentials  can  be  calculated  on  the  basis  of  a  tooth 
stress  of  about  35,000  pounds  per  square  inch  under  low  gear 
and  full  engine  power,  if  the  gears  are  made  of  carbon  steel, 
heat  treated.  The  stress  may  seem  high,  but  it  must  be  re- 
membered that  the  calculation  is  based  on  the  full  engine  power, 
whereas  from  15  to  25  per  cent,  of  the  engine  power  will  be 
lost  in  the  change  gear,  universal  joints  and  rear  axle  bevel 
gears.  Moreover,  in  very  powerful  cars  the  adherence  of  the 
driving  wheels  to  the  ground  limits  the  load  which  can  be 
placed  on  the  differential  to  a  figure  smaller  than  is  obtained  by 


FIG.    i2i.— END   ELEVATION   OF   SPUR   DIFFERENTIAL,   HALF   SEC- 
TIONED. 

multiplying  the  engine  torque   by   the   reducing  factor   between 
engine  and  rear  axle. 

The  master  gears  may  be  made  of  a  pitch  diameter  of  from 
3  to  4  inches,  at  the  option  of  the  designer  or  according  to 
the  size  of  the  driven  bevel  gear,  and  either  three  or  four  sets 
of  pinions  may  be  used.  We  will  illustrate  their  calculation  by 
the  example  of  a  differential  gear  for  a  four  cylinder  4x5  inch 
motor  and  the  reduction  ratios  mentioned  above.  We  found 
the  maximum  rear  axle  torque  to  be  1,490  pounds-feet.  We 


THE  DIFFERENTIAL  GEAR.  189 

will  assume  that  the  master  gears  have  a  3^  inch  pitch  diam- 
eter and  8-10  pitch  stub  teeth.  The  pitch  line  pressure  then 
will  be 

1,490  X  12 

Assuming  that  there  are  eight  pinions,  this  pressure  is  trans- 
mitted by  eight  teeth,  and  the  pressure  on  each  is 

«»«?  =  1,277  pounds. 
8 

Assuming  the  pinion  to  have  10  teeth,  for  which  the  constant  is 
0.041,  the  necessary  width  of  face  is 


=  o  .  89  —  say,  y*  inch  . 


0.041  X  35»ooo 

The  cases  for  spur  gear  differentials  are  made  in  two  parts 
which  are  held  together  by  bolts.  The  halves  should  preferably  be 
provided  with  a  telescoping  joint,  to  insure  the  continued  align- 
ment of  all  parts.  One  part  is  usually  made  in  the  form  of  a 
circular  plate,  and  the  other  in  the  form  of  a  cylinder  open  at 
one  end.  Sometimes  the  driven  bevel  gear  or  sprocket  is 
bolted  to  a  flange  on  the  cylindrical  part,  and  the  two  parts 
of  the  housing  are  held  together  by  means  of  through  bolts. 
In  another  design  the  cylindrical  part  has  a  flange  at  its  open 
end,  and  bolts  are  passed  through  this  flange,  the  end  plate  of 
the  differential  housing  and  the  web  of  the  bevel  gear,  as 
shown  in  Fig.  120. 

The  lighter  spur  differentials  sometimes  have  no  regufar  hous- 
ing, the  end  bearing  plates  being  held  together  by  bolts  and 
separated  by  spacers  surrounding  the  bolts. 

Lately  a  number  of  designs  of  differential  gears  have  been 
brought  out  which  prevent  a  car  from  losing  traction  when  one 
wheel  stands  on  slippery  ground.  Most  of  them  involve  some 
form  of  one-way  transmission  device,  that  is,  a  mechanism 
through  which  power  can  be  transmitted  in  one  direction  but 
not  in  the  other.  With  the  ordinary  differential,  if  one  wheel 
is  held  from  rotating  and  the  frame  or  housing  of  the  differ- 
ential is  rotated,  the  other  wheel  will  be  rotated  at  twice  the 
speed  of  the  differential  frame.  Also,  if  the  housing  is  held 
from  rotation  and  one  wheel  is  rotated,  the  other  wheel  will 
rotate  in  the  opposite  direction  at  the  same  speed.  With  one 
of  the  special  differentials,  if  one  wheel  is  locked  or  held  from 
rotating,  by  turning  on  the  other  wheel  the  housing  may  be 
rotated,  but  it  is  impossible  to  turn  the  free  road  wheel  by  turn- 
ing on  the  housing. 


190 


THE  DIFFERENTIAL  GEAR. 


It  is  self-evident  that  such  a  differential  does  not  equally 
divide  the  torque  between  the  two  driving  wheels,  for  if  it  did, 
then,  when  one  wheel  was  spinning,  the  other  wheel  would 
have  no  more  torque  impressed  upon  it  than  the  spinning  one, 
which  would  be  insufficient  to  propel  the  car.  The  relative 
torques  impressed  upon  the  two  wheels  respectively  depend 
upon  the  resistance  encountered  by  them.  Ordinarily  in 
straight-ahead  motion,  both  wheels  encounter  substantially 
equal  resistances,  and  the  driving  torque  on  both  is  therefore 
the  same.  But  in  turning  a  corner  the  outer  wheel  is  com- 


FIG.  122.— M  &  S  HELICAL  DIFFERENTIAL  GEAR. 

pelled  to  run  ahead  of  the  differential  housing  or  frame,  and 
all  the  torque  is  taken  by  the  inner  wheel,  the  conditions  then 
being  the  same  as  when  one  wheel  has  no  traction. 

One  of  the  best  known  of  these  special  differentials  is  the 
M  &  S,  illustrated  in  Fig.  122.  Each  of  the  axle  shafts  carries 
a  helical  gear  and  the  differential  spider  carries  three  helical 
pinions  with  radial  axes  and  six  such  pinions  of  which  each 
one  meshes  both  with  one  of  the  radial  pinions  and  with  one  of 
the  gears  on  the  axle  shafts.  It  is  well  known  that  in  helical 
gears,  if  the  angle  of  spiral  of  the  driving  gear  is  very  small, 
power  cannot  be  transmitted  through  the  pair  in  the  reverse 


THE  DIFFERENTIAL  GEAR. 


191 


direction,  because  the  frictional  resistance  is  too  great,  and  this 
is  the  principle  made  use  of  in  this  differential. 

Gearless  Differential — From  the  above  it  will  be  gathered 
that  the  special  feature  of  these  differentials  is  that  it  is  im- 
possible to  transmit  motion  from  the  differential  spider  to  one 
of  the  side  members.  Differentials  embodying  this  feature  can 
also  be  made  without  the  use  of  toothed  gears,  and  one  such 
design  is  illustrated  in  Pig.  123.  The  right  and  left  ratchets, 
which  are  keyed  to  their  respective  axle  shafts,  are  independent 
and  free  to  rotate  inside  of  the  housing.  The  two  round  mem- 
bers with  knobs  at  their  ends  and  centre  are  the  pawls  which 
form  the  interlocking  media  between  the  driving  sectors  and 
ratchets.  The  right  hand  view  shows  the  right  hand  end  of 
the  top  pawl  in  a  tooth  of  the  right  hand  ratchet,  being  driven 
by  the  contact  face  of  the  driving  sector  and  driving  the 


FIG.  123.— GEARLESS  DIFFERENTIAL. 


ratchet  forward.  In  the  same  manner  the  left  ratchet  is  driven 
forward  by  the  lower  pawl,  which  is  engaged  at  its  left  end. 
Thus  both  wheels  are  driven  forward  positively  and  neither 
can  spin,  as  with  the  common  differential. 

To  drive  backwards,  the  differential  housing  starts  to  move 
to  the  left  and  pushes  the  end  of  the  pawl  out  of  the  ratchet 
tooth,  which  throws  the  opposite  end  of  the  pawl  down  into 
the  tooth  of  the  opposite  ratchet.  The  contact  face  of  the  re- 
verse driving  sector  engages  and  drives  the  wheel  backward. 
The  lower  pawl  acts  in  the  same  manner.  In  turning  a  corner, 
imagine  that  the  car  is  being  driven  forward  and  is  to  be 
turned  to  the  left.  The  right  wheel  starts  to  revolve  faster 
than  the  left  and  causes  the  right  hand  ratchet  to  move 
faster  than  the  differential  housing,  which  latter  can  only  go 


192 


THE  DIFFERENTIAL  GEAR. 


as  fast  as  the  inner  or  slower  moving  wheel.  The  ratchet 
pushes  the  end  of  the  pawl  out  of  its  tooth  thus  allowing  the 
ratchet  to  have  a  free  movement  forward.  As  soon  as  the  cor- 
ner has  been  made  and  both  wheels  are  revolving  at  equal 
speed,  the  spring  at  the  centre  of  the  pawl  pushes  the  end  of 
the  pawl  back  into  engagement  and  the  drive  is  again  taken 
up  by  both  wheels. 

When  the  wheels  propel  the  drive  shaft,  as  in  case  of  coast- 
ing or  braking  through  it,  both  ratchets  start  to  turn  faster 


FIG.  124. — DIFFERENTIAL  LOCK. 


than  the  housing,  and  push  the  engaged  ends  of  the  pawl  out 
of  engagement  and  the  opposite  ends  into  the  driving  position 
in  the  opposite  ratchet  teeth,  thus  causing  the  ratchets  to 
propel  the  drive  shaft. 

Differential  Lock. — A  few  of  the  heavier  designs  of  trucks 
are  provided  with  differential  locks  which  enable  the  driver  to 
put  the  differential  gear  out  of  operation  at  will.  The  problem 
of  working  out  a  neat  and  all  round  satisfactory  differential  lock 
presents  considerable  difficulty,  which  is  probably  the  reason  that 
this  device  is  not  more  extensively  used.  Fig.  124  illustrates  a 
differential  lock  of  typical  design.  A  jaw  clutch  is  provided, 
sliding  on  a  squared  section  of  one  of  the  differential  shafts,  by 
which  the  differential  housing  may  be  locked  to  this  shaft. 


CHAPTER  VIII. 


UNIT   POWER  PLANTS   AND   TRANSMISSION   AXLES. 

When  a  line  of  shafting  is  supported  in  several  bearings,  it 
Is  necessary  to  either  mount  all  of  the  bearings  in  absolute 
alignment  and  keep  them  so,  or  to  make  the  shaft  in  sections 
and  connect  the  sections  by  universal  joints.  In  an  automobile 
power  plant  we  have  such  a  line  of  shafting  extending  through 
the  motor  and  change  gear  box,  which  may  be  supported  by 
from  four  to  ten  bearings.  It  is  an  easy  matter  to  keep  all  of 
the  bearings  in  the  crankcase  or  those  in  the  gear  case  in 
alignment.  However,  it  is  virtually  impossible  to  insure 
continued  alignment  of  the  gear  box  bearings  with  those  of 
the  crankcase  if  the  two  cases  are  mounted  separately  on  a 
light  pressed  steel  frame,  as  is  customary.  Owing  to  the  severe 
shocks  and  wrenches  which  it  receives  in  driving  at  speed  over 
rough  roads,  the  frame  "weaves"  and  distorts  and  cannot  at 
all  be  depended  upon  to  maintain  the  bearings  in  alignment. 

Two  courses  are  open  to  the  designer  for  overcoming  this 
difficulty.  He  may  either  connect  the  crankshaft  to  the  primary 
shaft  of  the  gear  box  through  a  double  universal  and  sliding 
joint,  or  he  may  tie  the  gear  box  to  the  crankcase  in  such  a 
manner  that  the  whole  forms  a  single  rigid  structure.  The 
former  arrangement  permits  of  slight  displacements  of  one  of 
the  cases  with  respect  to  the  other  in  every  direction.  The  second 
arrangement  gives  what  is  known  as  the  unit  power  plant,  which 
is  used  more  especially  on  low  and  moderately  powered  cars. 

What  is  perhaps  the  most  common  type  of  unit  power  plant 
is  illustrated  in  Fig.  125.  Engine,  clutch  and  gear  box  are  located 
in  their  usual  relative  positions,  the  gear  box  being  brought  as 
close  to  the  engine  as  possible.  The  crankcase  is  provided  at 
the  rear  with  a  flat  cylindrical  extension  designed  to  house  the 
flywheel.  This  extension  has  a  flange  at  its  open  end  to  which 
the  gear  box  is  bolted,  the  latter  being  formed  with  a  forward 

193 


194    UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES. 


UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES.  195 

extension  designed  to  house  the  friction  clutch.  The  exact  loca- 
tion of  the  vertical  joint  varies  somewhat  in  the  different  de- 
signs, but  a  common  feature  of  this  type  of  unit  power  plant 
is  that  the  entire  unit  may  be  separated  into  two  parts  longi- 
tudinally and  forms  three  chambers,  for  the  engine  crankshaft, 
for  the  flywheel  and  clutch,  and  for  the  change  gear,  respectively. 
Of  course  the  crankcase  may  be  divided  horizontally  through 
the  centre  of  the  crankshaft,  but  the  tendency  is  to  use  barrel 
type  crankcases  in  connection  with  this  type  of  unit  power  plant. 
In  practically  all  unit  power  plants  the  two  shafts  of  the  change 
speed  gear  lie  in  a  vertical  plane,  this  arrangement  tending  to 
greater  symmetry  of  the  whole  design. 

Access  to  the  crankshaft  bearings  is  afforded  by 'either  a  re- 
movable bottom  plate  of  the  crankcase  or  large  hand-hole  cover 
plates  on  one  side,  while  the  interior  of  the  clutch  and  gear 
compartments  may  be  reached  through  large  hand-holes. 

Among  the  advantages  of  such  a  unit  power  plant  may  be  men- 
tioned the  fact  that  it  simplifies  the  construction  in  that  it  ob- 
viates the  need  of  a  double  universal  joint  between  the  engine 
and  change  gear  and  makes  it  possible  to  support  the  whole  unit 
upon  the  frame  at  three  or  four  points  instead  of  an  equal  num- 
ber of  supports  for  either  part.  Moreover,  the  complete  en- 
closure of  all  moving  parts  tends  to  the  reduction  of  noise,  to 
increased  cleanliness  and  to  better  lubrication  and  protection  of 
wearing  parts  from  dust  and  grit.  The  change  gear  is  brought 
somewhat  closer  to  the  engine  and  is  therefore  likely  to  come 
in  a  more  accessible  position  underneath  the  front  seat  floor 
boards.  However,  the  main  object  of  unit  construction  and  its 
chief  advantage  is  that  if  the  bearings  are  once  properly  lined 
up,  they  will  remain  in  alignment,  and  hence  there  is  no  danger 
of  binding  and  consequent  injury  to  the  bearings. 

Three  Point  Support. — Although  the  three  point  support  is 
applicable  to  engines  and  gear  boxes  mounted  separately,  it 
is  specially  advantageous  in  the  case  of  unit  power  plants.  The 
principle  involved  in  the  three  point  support  is  perhaps  best  ex- 
plained by  reference  to  a  three  legged  stool  which  will  stand 
securely  on  an  uneven  floor,  whereas  a  four  legged  one  will 
not.  In  a  motor  car,  if  the  frame  supporting  the  power  plant 
should  be  distorted,  it  would  not  subject  the  case  and  arms  to 
any  stress  if  the  power  plant  were  supported  at  three  points, 
whereas  if  it  was  supported  at  four  points  the  rigidity  of  the 
case  and  its  arms  would  resist  distortion  of  the  frame,  and 
hence  these  parts  would  be  severely  stressed  by  distorting  in- 


196 


UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES. 


UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES.    197 

fluences.  Crankcases  and  gear  boxes  supported  at  four  points 
are  sometimes  broken  by  excessive  road  strains  on  the  frame. 

In  Fig.  125  the  power  plant  has  one  point  of  support  at  the  front, 
a  cross  member  of  the  frame  passing  underneath  the  crankcase, 
and  having  the  latter  fastened  down  to  it  by  two  bolts  located  close 
together  at  the  middle  of  the  crankcase  bottom.  The  other  two 
points  of  support  are  at  the  side  of  the  flywheel  housing,  which  is 
cast  with  laterally  extending  arms  which  rest  on  top  of  the  sub- 
frame  or  connect  through  hangers  with  the  main  frame.  An 
alternate  method  consists  in  casting  the  crankcase  with  two 
lateral  supporting  arms  near  its  front  end  and  have  the  third 
point  of  support  at  the  rear  of  the  gear  box,  the  rear  bear- 
ing hub  of  the  latter  being  developed  in  the  form  of  a  sup- 
porting bracket  resting  on  a  cross  member  of  the  frame.  There 
are  two  distinct  arrangements  of  this  rear  support.  The 
simplest  consists  in  passing  two  long  bolts  through  the  rear 
bearing  hub  and  the  supporting  frame  cross  member.  This 
does  not  give  a  true  three  point  support,  as  there  are  in  reality 
two  points  at  the  rear,  but  since  they  are  comparatively 
close  together,  they  act  substantially  as  a  single  sup- 
port. In  order  to  obtain  a  single  support  at  the  rear,  the  rear 
bearing  hub  has  a  part  spherical  surface  turned  upon  it  which 
rests  in  a  spherical  socket  bolted  to  the  frame  cross-member. 
The  socket  must,  of  necessity,  be  made  in  halves,  and  for  con- 
venience in  machining  the  rear  bearing  hub  is  made  separate 
and  bolfed  to  the  casing.  A  similar  supporting  method  may  be 
applied  to  the  front  bearing  of  the  engine. 

Of  course,  where  a  supporting  arm  has  a  large  flat  bearing 
surface  and  is  bolted  down  to  the  supporting  member  it  is 
not  quite  correct  to  speak  of  a  "point"  of  support.  In  such  a 
case  there  are  in  reality  three  or  four  supporting  surfaces  in- 
stead of  three  or  four  points  of  support,  and  it  is  easily  seen 
that  if  the  surfaces  of  a  "three  point  support"  are  fairly  large 
there  must  still  be  considerable  strain  in  the  material  near  the 
supporting  surfaces  if  the  frame  is  distorted.  In  order  to 
eliminate  these  strains  as  far  as  possible  the  Midland  Motor 
Car  Company  makes  the  two  forward  supports  of  the  power 
plant  on  the  main  frame  in  the  form  of  trunnions  and  sliding 
blocks,  the  trunnions  being  formed  on  the  ends  of  a  trussed  cross 
member  and  the  blocks  sliding  in  the  channel  of  the  frame. 
The  latter  is  "swept  in"  in  front,  which  allows  the  cross  member 
to  be  inserted  into  the  frame  channel  from  the  rear. 


198    UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES. 


UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES.  199 

Flywheel  in  Front  — One  of  the  chief  difficulties  encountered 
in  combining  the  engine  and  the  change  gear  in  a  single  unit 
is  due  to  the  fact  that  the  flywheel  is  located  between  them 
and  to  enclose  it  requires  a  great  deal  of  metal,  adding  both 
to  the  weight  and  the  cost  of  the  car.  In  four  cylinder  motors 
there  is  a  tendency  to  use  a  flywheel  of  rather  inadequate  capacity 
when  it  is  to  be  enclosed,  which  somewhat  detracts  from  the 
steady  running  qualities  of  the  car.  To  overcome  this  difficulty 
two  expedients  may  be  resorted  to.  The  first  consists  in  placing 
the  flywheel  at  the  front  of  the  engine,  as  shown  in  Fig.  126. 
This  eliminates  the  flywheel  housing,  and  permits  of  bringing 
the  gear  box  considerably  closer,  but  there  are  also  a  number 
of  objections  to  this  practice.  Its  purpose  being  to  equalize  the 
torque  of  the  engine  before  it  is  transmitted  to  the  change  gear, 
the  logical  place  for  the  flywheel  seems  to  be  between  these  two 
parts.  The  crankshaft  and  its  bearings  are  undoubtedly  sub- 
jected to  more  severe  usage  with  the  flywheel  located  in  front. 
With  the  very  considerable  weight  of  the  flywheel  almost  directly 
over  the  front  axle  the  strains  on  the  front  tires  are  increased. 
However,  with  the  flywheel  in  this  position  its  diameter  is  less 
closely  limited,  and  some  manufacturers  use  the  front  mounted 
flywheel  as  a  radiator  fan.  With  this  construction  the  timing 
gears  of  the  engine  are  usually  placed  at  the  rear  end,  where 
they  are  more  accessible. 

An  alternate  construction  consists  in  joining  the  crankcase 
and  gear  box  by  a  yoke  running  around  the  flywheel,  as  illus- 
trated in  Fig.  127.  Either  both  cases  and  the  yoke  may  be  cast 
in  a  single  piece;  half  of  the  yokes  may  be  cast  with  either  case 
(as  in  Fig.  127),  or  the  yoke  pieces  may  be  separate  and  secured 
to  the  two  cases  by  cap  screws  or  bolts.  This  method  enables 
a  saving  in  weight  to  be  effected  as  compared  with  that  illus- 
trated in  Fig.  125,  and  is  free  from  the  objections  urged  against 
the  front  mounted  flywheel.  It  has  been  adopted  on  several 
American  cars  in  recent  years.  The  yoke  around  the  flywheel 
is  conveniently  situated  for  supporting  the  bearing  for  the  clutch 
and  brake  pedal  shaft. 

Unit  power  plant  construction  has  become  extremely  popular 
in  this  country. 

Transmission  Axles  — Instead  of  combining  the  gear  box  with 
the  engine,  some  makers  secure  it  rigidly  to  the  rear  axle 
housing,  thus  forming  what  is  known  as  a  transmission  axle. 
The  leading  exponent  in  America  of  this  system  of  construction 
has  been  the  Packard  Co.  The  advantages  of  this  arrange- 


200  UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES. 

ment  are  that  it  does  away  with  a  separate  gear  box,  thus  elim- 
inating one  unit,  that  it  permits  of  using  a  comparatively  long 
propeller  shaft  whose  angularity  will  not  vary  much  under  the 
play  of  the  body  springs  and  the  absolute  value  of  which  will 
always  be  small,  and  that  the  propeller  shaft  and  universal  joint 


FIG.  128. — SECTIONAL  VIEW  OF  PACKARD  CHANGE  GEAR  AND  REAH 

AXLE  DRIVE  (OLD  MODEL). 

run  always  at  engine  speed,  and  are  never  subjected  to  any 
greater  torque  than  the  maximum  of  which  the  engine  is  capable, 
hence  they  can  be  made  somewhat  lighter.  Besides  this,  the 
system  does  away  with  two  or  more  universal  joints  in  the 
transmission  line,  requiring  the  use  of  only  one  such  joint  on 


UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES.    201 


at  most  two.  The  chief  disadvantage  of  the  transmission  axle 
is  that  it  materially  increases  the  unsprung  weight  supported  by 
the  rear  wheels  and  tires,  and  thus  tends  to  increase  the  wear 
of  the  tires.  Some  difficulty  is  also  met  with  in  arranging  the 
control  connections  between  the  change  gear  lever  on  the  spring 
supported  frame  and  the  sliding  bars  in  the  unsprung  gear  box 
in  such  a  manner  that  the  play  of  the  springs  will  neither  affect 
the  position  of  mesh  of  the  sliding  gears  nor  cause  the  control 
lever  to  move  on  its  sector  or  quadrant  and  produce  an  un- 
pleasant rattle. 

The  majority  of  the  transmissions  built  together  with  the  rear 
axle  are  of  the  three  speed  and  reverse  selective  sliding  type. 
It  is  important  that  the  length  of  the  gear  box  be  kept  as  small 
as  possible  so  that  the  moment  of  its  weight  around  the  axis 
of  the  rear  axle  may  not  be  too  great.  Those  types  of  reversing 
gears  which  economize  space  in  the  longitudinal  direction  are 
therefore  particularly  suitable  for  rear  axle  gear  boxes.  In 


FIG.  129. — GEAR  Box  ON  FORWARD  END  OF  TORQUE  TUBE. 

these  gear  boxes  the  two  shafts  usually  lie  in  a  horizontal  plane 
(Fijj.  128),  since  it  is  not  practicable  to  place  the  secondary 
below  the  primary  shaft,  as  that  would  reduce  the  road  clearance 
too  much,  and  the  secondary  shaft  cannot  well  be  on  top,  since  it 
is  desirable  to  have  the  secondary  gears  run  in  oil  and  the  height 
of  the  oil  in  the  case  is  limited  by  the  level  of  the  protruding 
shafts.  The  constantly  meshed  gears  and  direct  drive  clutch  are 
generally  placed  at  the  rear,  as  some  space  in  the  longitudinal 
direction  can  be  saved  in  this  way. 

An  arrangement  of  the  gear  box  which  affords  some  of  the 
advantages  of  the  transmission  axle  and  does  away  with  some 
of  its  disadvantages  is  illustrated  in  Fig.  129.  The  gear  box 
and  rear  axle  here  also  form  a  unit,  the  two  being  connected 
by  the  propeller  shaft  tube,  or  torque  tube,  and  the  gear  box 
hung  from  a  cross  member  of  the  frame  by  a  ball  and  socket 
joint  at  its  forward  end.  As  in  the  case  of  transmission  axles, 


202    UNIT  POWER  PLANTS  AND  TRANSMISSION  AXLES. 

the  angle  between  the  two  members  of  the  universal  joint  varies 
but  little  and  is  always  small.  Most  of  the  weight  of  the  gear 
box  is  spring-supported  and  although  it  changes  its  position 
relative  to  the  frame  as  the  body  springs  compress  and  extend, 
this  change  in  position  is  relatively  much  smaller  and  the  difficulty 
of  properly  connecting  up  the  control  lever  is  correspondingly 
reduced. 

Straight  Line  Drive — The  last  two  mentioned  arrangements 
of  the  gear  box  lend  themselves  particularly  to  that  form  of 
construction  known  as  the  straight  line  drive — that  is,  such  an 
arrangement  of  the  different  parts  that  when  the  car  carries  a 
normal  load  the  engine  crankshaft,  gear  box  primary  shaft  and 
propeller  shaft  are  in  a  straight  line.  Under  these  conditions 
motion  is  transmitted  uniformly  through  a  single  universal  joint, 
and  owing  to  the  relatively  large  distance  between  the  rear  axle 
and  the  universal  joint  the  play  of  the  body  springs  has  little 
influence  on  the  drive.  In  order  to  insure  this  straight  line 
relation  of  crankshaft  and  propeller  shaft  it  is  generally  neces- 
sary to  carry  the  engine  in  a  slightly  tilted  position,  with  the  rear 
end  somewhat  lower  than  the  front,  as  if  the  engine  crankshaft 
were  placed  at  the  same  level  as  the  rear  axle  shafts  the  engine 
flywheel  would  not  clear  the  ground  sufficiently.  In  all  con- 
structions in  which  there  is  only  a  single  universal  joint  in  the 
propeller  shaft,  a  substantially  straight  line  drive  should  be 
aimed  at,  for,  as  shown  in  the  chapter  on  Universal  Joints, 
when  the  two  shafts  make  an  appreciable  angle  with  each  other 
there  are  serious  fluctuations  in  the  ratio  of  transmission,  and 
consequently  the  transmission  parts,  and  particularly  the  tires, 
are  subjected  to  extra  severe  strains. 


CHAPTER  IX. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

At  present  the  great  majority  of  pleasure  cars  are  driven 
through  a  shaft  and  bevel  gears.  The  advantages  of  this  drive 
are  that  it  can  readily  be  completely  enclosed,  oil  and  dustproof, 
and  that  it  is  reasonably  efficient  and  noiseless.  Any  desired  gear 
reduction  up  to  5  to  1  can  easily  be  obtained.  A  disadvantage 
of  the  bevel  gear  drive,  as  compared  with  the  chain  drive,  is 
that  with  the  former  it  is  difficult  to  provide  more  than  one  gear 
ratio. 

The  two  chief  elements  of  a  shaft  drive  are  the  propeller 
shaft  and  the  bevel  gearset.  The  drive  also  comprises  either  one  or 
two  universal  joints.  It  was  shown  in  a  previous  chapter  that 
two  such  joints  are  necessary  if  an  absolutely  uniform  transmis- 
sion of  motion  from  the  gear  box  or  engine  to  the  rear  axle  is 
required,  and  on  the  higher  grades  of  cars  two  universals  are 
generally  employed.  However,  by  making  the  propeller  shaft 
comparatively  long,  and  placing  the  gear  box  and  rear  axle  in 
such  relation  to  each  other  that  when  the  vehicle  carries  a  normal 
load,  the  primary  shaft  of  the  change  gear  and  the  propeller 
shaft  are  nearly  in  line,  many  designers  get  along  with  a  single 
universal,  which  they  insert  between  the  transmission  tail  shaft 
and  the  propeller  shaft. 

Types  of  Rear  Axles. — Rear  axles  are  divided  into  live 
and  dead  axles.  A  live  axle  is  an  axle  through  which  the  pro- 
pelling power  is  transmitted  to  the  driving  road  wheels,  and  a 
dead  axle  is  one  which  merely  Carries  the  weight  of  the  frame 
and  body.  Cars  driven  by  shaft  and  bevel  gears,  shaft  and  worm 
gears,  or  by  a  single  chain,  have  live  axles,  whereas  cars  driven 
by  double  (side)  chains  have  dead  axles. 

A  live  axle  has  two  principa1  functions  to  perform,  viz.,  to 
support  the  weight  carried  upon  the  rear  springs,  and  to  transmit 
the  power  to  the  road  wheels.  These  two  functions  can  be  per- 
formed by  a  simple  revolving  axle,  but  in  that  case  the  direc- 

203 


204 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  205 

tion  of  the  stress  due  to  the  weight  carried  changes  constantly, 
and  since  the  resistance  of  the  material  is  greatly  lessened  if 
the  stress  alternates  in  direction,  it  is  much  preferable  to  support 
the  weight  on  non-rotating  parts.  Some  of  the  earlier  shaft  and 
single  chain  driven  cars  had  rear  axles  consisting  merely  of  a  , 
revolving  shaft  running  in  bearings  secured  to  the  body  springs. 
The  axle  had  one  road  wheel  rigidly  secured  to  it,  the  other 
wheel  being  secured  to  a  sleeve  free  upon  the  shaft;  one  master 
gear  of  the  differential  was  secured  to  the  shaft,  and  the  other 
to  the  sleeve.  However,  for  the  reason  above  stated,  practically 
all  modern  live  axles  comprise  one  part — the  housing — for  sup- 
porting the  load,  and  another — the  axle  shafts — for  transmitting 
the  power. 

In  the  normal  operation  of  a  car  there  are  three  distinct 
sources  of  stress  in  a  rear  axle,  viz.,  the  weight  of  the  frame 
and  body  resting  on  the  axle,  the  bearing  load  due  to  the  bevel 
gear  tooth  pressure,  and  the  torsion  on  the  axle  shafts.  An 
axle  in  which  all  of  these  stresses  come  on  the  axle  shafts  is 
known  as  a  plain  live  axle.  An  axle  in  which  the  axle  shafts  are 
subjected  only  to  torsional  stress  and  the  stress  due  to  the  weight 
of  the  frame  and  body,  is  known  as  a  semi-floating  axle,  and  an 
axle  in  which  the  shafts  are  relieved  of  all  except  torsional 
stress,  is  known  as  a  full  floating  axle. 

Each  rear  axle  has  two  sets  of  bearings,  viz.,  those  supporting 
the  differential  and  those  through  which  the  axle  is  supported' 
in  the  road  wheels.  The  former,  which  we  may  call  the  differ- 
ential bearings,  are  subjected  to  a  load  due  to  the  tooth  pressure 
of  the  bevel  driving  gears,  while  the  latter  are  subjected  to  a 
load  due  to  that  part  of  the  weight  of  the  frame  and  body  which 
rests  on  the  rear  springs.  It  is  directly  apparent  that  in  the  plain 
live  axle,  illustrated  in  Fig.  130,  the  load  due  to  the  bevel  gear 
tooth  pressure  is  taken  up  by  the  axle  shafts,  as  is  the  load  due 
to  the  weight  of  the  rear  part  of  the  car.  The  stress  in  the 
shafts  due  to  these  loads  reverses  twice  every  revolution  of  the 
axle,  and  since  it  adds  to  the  torsional  stress  of  driving,  it  can 
readily  be  seen  that  the  axle  shafts  in  this  type  of  axle  must  be 
made  very  rugged  in  order  to  stand  up  to  the  work.  As  a 
matter  of  fact,  axle  breakages  were  rather  frequent  when  axles 
of  this  type  were  common. 

In  the  semi-floating  axle  illustrated  in  Fig.  131  the  axle  shafts 
are  relieved  of  the  bevel  gear  tooth  pressure.  This  is  accom- 
plished by  carrying  the  differential  gear  directly  in  bearings  in 
the  axle  housing,  instead  of  supporting  it  upon  the  axle  shafts. 


206          BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.          207 

The  latter  are  made  somewhat  smaller  in  diameter  than  the  bore 
of  the  hubs  of  the  differential  housing,  and  pass  through  these 
hubs  without  contacting  with  them,  establishing  driving  connec- 
tion with  the  differential  master  gears  by  square,  hexagonal  or 
fluted  driving  joints. 

The  next  step  in  axle  development  was  to  relieve  the  outer 
end  of  the  axle  shafts  of  bending  stress,  in  the  same  way  as 
the  inner  ends.  This  is  accomplished  (see  Fig.  132)  by  extending 
the  axle  tubes  entirely  through  the  wheel  hubs,  and  mounting 
the  wheel  bearings  on  the  outside  of  these  tubes,  so  that  the 
weight  load  is  transmitted  directly  from  the  axle  housing  to  the 
wheel  hub.  The  axle  shafts  extend  through  the  housing,  and 
their  outer  ends  connect  with  the  wheel  hubs  through  driving 
dogs  or  positive  clutches.  With  an  axle  of  this  design  it  is  possi- 
ble to  entirely  withdraw  the  driving  shafts  from  the  axle  without 
removing  the  axle  from  the  car. 

An  intermediate  type  between  the  full  floating  and  semi-floating 
axles  has  recently  been  used  to  some  extent,  differing  from  the 
full  floating  in  that  its  shafts  are  rigidly  connected  to  the  wheel 
hubs — which  latter  are  mounted  on  bearings  on  the  outside  of 
the  axle  housing — by  driving  flanges  bolted  to  the  wheel  hubs, 
and  either  forged  integral  with  the  axle  shafts  or  securely  keyed 
thereto.  In  an  axle  of  this  type  the  shafts,  although  relieved  of 
weight  carrying  loads,  are  subjected  to  endwise  stresses  due  to 
skidding,  and  it  has  been  suggested  to  call  these  three-quarter 
floating  axles.  In  a  three-quarter  floating  axle  there  is  only  one 
bearing  in  each  wheel  hub,  which  results  in  economy  of  manu- 
facture. There  is  also  less  strain  on  the  bearings  from  lateral 
shocks  on  the  wheels  than  in  a  full  floating  axle. 

Full  floating  axles  in  which  the  shafts  are  entirely  relieved  of 
all  but  torsional  stresses  are  generally  regarded  as  the  most 
highly  developed  type,  and  are  widely  used  on  high  grade  cars. 
They  are  more  expensive  to  manufacture  than  semi-floating  and 
plain  live  axles. 

Shaft  Materials. — Propeller  shafts  and  rear  axle  driving 
shafts  may  be  made  from  30  point  carbon  steel,  45  point  carbon 
steel,  30  point  carbon  3l/2  per  cent,  nickel  steel,  vanadium  steel  or 
chrome  nickel  steel.  In  each  case  the  material  must  be  heat 
treated,  as  a  suitable  heat  treatment  almost  doubles  the  elastic 
limit  in  some  instances.  The  heat  treatment  generally  consists 


208 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


I 
k 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.          209 

in  quenching  the  steel  in  oil  at  a  suitable  temperature,  and  then 
reheating  it  to  a  certain  lower  temperature  from  which  it  is 
cooled  slowly.  Thus  the  standards  committee  of  the  Society  of 
Automobile  Engineers  recommend  the  following  treatment  for 
35  point  carbon  steel :  After  forging  or  machining  heat  to 
1500°-1550°  Fahr.,  cool  slowly,  reheat  to  1450°-1500°  Fahr., 
quench,  reheat  to  600° -1200°  Fahr.,  and  cool  slowly.  The  higher 
the  reheating  temperature  the  tougher  the  steel  will  be,  but  the 
lower  the  reheating  temperature  the  greater  will  be  its  tensile 
strength.  The  steel  has  a  tensile  strength  of  50,000  pounds  per 
square  inch  in  the  annealed  condition,  and  about  twice  that  when 
heat  treated  and  drawn  at  a  low  temperature.  For  the  45  point 
carbon  steel  the  same  heat  treatment  is  recommended.  In  both 
cases  the  parts  may  be  machined  after  they  have  cooled  from  the 
first  heating.  The  45  point  carbon  steel  attains  a  tensile  strength 
of  125,000  pounds  when  drawn  at  a  low  temperature  and  95,000 
pounds  when  drawn  at  a  high  temperature.  The  elastic  limit 
of  this  steel  when  heat  treated  varies  between  90,000  pounds 
and  60,000  pounds.  The  heat  treatment  for  the  3^  per  cent, 
nickel  steel  is  comparatively  simple,  consisting  in  heating  to 
1500°-1600°  Fahr.,  quenching,  heating  to  600°-1200°  Fahr.,  and 
cooling  slowly.  This  treatment  increases  the  elastic  limit  of  the 
steel  from  55,000  to  as  much  as  160,000  pounds  per  square  inch. 
The  elastic  limit  of  chrome  nickel  steel  after  heat  treatment  may 
be  as  high  as  175,000  pounds  per  square  inch. 

The  heat  treatments  giving  the  extreme  elastic  limits  can- 
not, however,  be  used  for  transmission  shafts,  which  must  be 
made  of  relatively  tough  material  and  also  must  be  worked 
after  being  heat  treated,  which  means  that  the  material  must 
not  be  too  hard  to  machine  satisfactorily.  An  elastic  limit  of 
100,000  Ibs.  per  square  inch  for  nickel  steel  and  120,000  Ibs. 
per  square  inch  for  chrome  nickel  steel  is  about  all  that  is 
generally  obtained  in  shafting  material.  That  the  elastic  limit 
even  of  steel  of  the  same  denomination  may  greatly  vary  with 
the  composition  and  the  heat  treatment  is  shown  by  figures 
given  in  a  paper  read  before  the  American  Society  of  Me- 
chanical Engineers  by  John  Younger,  of  the  Fierce-Arrow 
Motor  Car  Company.  This  concern,  in  its  5-ton  trucks,  orig- 
inally used  rear  axle  shafts  made  of  chrome  nickel  steel  con- 
taining 0.20%  carbon,  1.5%  chromium,  0.30%  manganese,  4% 
nickel,  0.20%  silicon  and  less  than  0.04%  phosphorus  and 
sulphur,  which  showed  an  elastic  limit  of  90,000  Ibs.  per  square 
inch  and  an  ultimate  strength  of  105,000  Ibs.  per  square  inch. 
These  shafts  gave  trouble  by  breaking  at  the  ends  of  the  fluted 


210  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

portion,  and  another  steel  was  then  substituted  containing 
0.30%  carbon,  0.50%  manganese,  1.5%  chromium  and  3.5% 
nickel,  which  after  heat  treatment  showed  an  elastic  limit  of 
175,000  Ibs.  per  square  inch  and  an  ultimate  strength  of 
185,000  Ibs.  per  square  inch.  This  proved  entirely  satisfactory. 

Higher  grades  of  steel  are  usually  employed  in  the  rear 
axle  drive  shafts  than  in  the  propeller  shaft,  for  the  reason 
that  an  increase  in  the  diameter  of  the  axle  shafts,  necessitat- 
ing a  corresponding  increase  in  the  diameter  of  the  axle  tubes, 
bearings,  etc.,  entails  a  comparatively  large  increase  in  weight, 
and  that  dead  weight.  Besides,  with  the  usual  reduction  ratios 
the  torque  on  each  rear  axle  shaft  is  twice  as  great  as  the 
torque  on  the  propeller  shaft,  or  more.  Of  fourteen  propeller 
shafts  investigated  by  Russell  Huff,  eleven  were  made  of 
medium  carbon  steel,  containing  for  the  most  part  0.35%  car- 
bon; two  were  made  of  chrome  nickel  steel  and  one  of  chrome 
vanadium  steel.  Of  the  rear  axle  shafts  of  the  same  cars  only 
one  was  of  carbon  steel,  while  eight  were  of  chrome  nickel 
steel,  four  of  nickel  steel  and  one  of  chrome  vanadium  steel. 
Mr.  Huff  calculated  the  factor  of  safety  in  each  case  and  found 
the  average  value  to  be  5.8  for  the  propeller  shafts  and  2.7 
for  the  rear  axle  shafts,  both  based  on  the  elastic  limits  of  the 
materials.  Half  of  the  cars  had  transmission  axles.  For  the 
other  half  the  average  propeller  shaft  factor  of  safety  was  only 
3.75. 

Calculation  of  Shaft  Diameters— Propeller  shafts  and  driv- 
ing shafts  of  full  floating  type  rear  axles  are  subjected  to  tor- 
sional  stresses  only,  and  may  therefore  be  calculated  by  the  same 
methods.  The  diameters  of  these  shafts  depend  to  quite  an  ex- 
tent upon  the  method  of  fastening  employed  at  their  ends. 
One  formerly  common  method  consists  of  milling  down  the 
ends  of  the  shaft  to  an  approximate  square  whose  width  of  face 
is  about  0.8  times  the  diameter  of  the  shaft,  and  broaching  out 
the  hub  of  the  universal  joint  fork,  etc.,  correspondingly.  Un- 
fortunately this  greatly  reduces  the  strength  of  the  shaft  at  the 
joints,  and  the  excess  strength  of  the  shaft  proper  is  absolutely 
useless.  The  square  portion  of  the  shaft  should  gradually  merge 
into  the  round  section,  in  order  that  there  may  be  no  concentra- 
tion of  stress  at  a  sudden  change  in  the  section.  The  strength 
of  the  square  portion  of  the  shaft  is  only  about  0.7  times  that 
of  the  full  shaft.  In  order  to  save  the  excess  weight  in  the 
propeller  shaft,  due  to  the  greater  torsional  strength  of  the  full 
round,  as  compared  with  the  square  section,  some  manufacturers 
use  propeller  shafts  of  square  section,  thereby  saving  about  20 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


211 


per  cent,  in  weight.    Hexagonal  joints  cause  less  loss  of  strength 
than  square  joints,  and  are  used  to  some  extent. 

A  second  method  of  fastening  the  universal  joint  forks,  gears, 
etc.,  to  the  shafts  consists  in  keying  them  to  a  tapered  seat.  This 
also  slightly  reduces  the  strength  of  the  shaft,  but  just  how  much 
can  only  be  conjectured.  The  most  approved  method  of  securing 
these  parts  to  driving  shafts  consists  in  fluting  the  shafts  and 
broaching  out  the  hubs,  using  either  four  or  six  flutes.  The  loss 
in  strength  due  to  the  flutes  is  considerably  less  than  that  due  to 
squaring  the  shaft.  If  it  is  desired  to  use  the  lightest  possible 
propeller  shaft,  or  rear  axle  driving  shafts,  the  ends  are  upset 
so  that  after  they  are  squared  or  fluted  they  are  at  least  the 
same  strength  as  the  circular  section  of  the  shaft  proper.  This 
practice  prevails  to  a  large  extent  in  the  manufacture  of  the 
highest  grade  of  cars. 

Tests  of  Fluted  Shafts — Comprehensive  torsion  tests  of 
plain  and  fluted  shafts  have  been  made  by  C.  E.  Larard,  whose  re- 
sults are  contained  in  a  paper  presented  to  the  Incorporated  In- 
stitution of  Automobile  Engineers  in  London  in  January,  1911. 
Mr.  Larard's  tests  covered  two 
materials,  viz.,  mild  steel  and 
nickel  steel.  These  tests  were 
made  more  particularly  with  a 
view  to  determine  the  strength  of 
fluted  shafts  for  change  gear 
boxes,  hence  the  use  of  mild  steel 
of  only  about  0.15  per  cent  car- 
bon. This  steel  is  suitable  for 
case  hardening,  a  treatment  re- 
quired by  sliding  gear  shafts,  but 
is  not  adapted  for  propeller  shafts 
owing  to  its  low  elastic  limit. 
The  results  are  here  given  to 
show  the  effect  of  fluting  on  the 
torsional  strength  of  shafts. 


FIG.  133. — SECTIONS  OF  FLUTED 


Mr.  Larard's  tests  on  carbon  steel  SHAFTS  TESTED... 

were  made  on  four  pairs  of  specimens,  one  specimen  of  each  pair 
having  six  keyways,  while  the  other  one  was  a  plain  cylinder  of  a 
diameter  equal  to  the  bottom  diameter  of  the  fluted  shaft.  The 
largest  fluted  shaft  was  of  2^  inches,  and  the  smallest  of  IJ4 
inches  outside  diameter,  the  corresponding  plain  shafts  were  of 
2  and  1  inch  diameter  respectively.  The  angular  extent  of  the 


212 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


keyways  is  shown  in  Fig.  133.    In  the  following  table  are  given 
the  most  important  results  of  the  tests  on  these  specimens. 

TABLE  VII.— TORSION  TESTS  OF  MILD  STEEL  SHAFTS. 


Diameter  of       Particulars  of 
Specimen.  Keyway. 

Out-      Bottom  of  Depth  at 

side,      Keyway,    Width, 
Ins.  Ins 


'eptl 
Edge, 
Ins. 


Limit  of 
Elasticity 

in 

Pounds - 
Inches. 


Torque  at 
Fracture 

in 

Pounds- 
Inches. 

155,000 
90,800 
57,700 
41,600 
38,000 
28,100 
16,550 
11,700 


Form 

Specimen.  Ins.  Ins. "        Ins. 

Fluted    24  2  i  A          16,100 

Plain    2  14,800 

Fluted    1W          Hf          A         A  7,400 

Plain    Hi  6,400 

Fluted    If  It  H         *  4,430 

Plain    Hi  4,850 

Fluted    li  1  i  *  2,750 

Plain    1  2,680 

Comparing  the  figures  of  the  several  pairs  in  the  above  table, 
it  will  be  seen  that  in  each  case  the  elastic  limit  of  the  plain  speci- 
mens is  slightly  less  than  that  of  the  fluted  specimens,  thus  show- 
ing that  some  strength  is  added  by  the  keys.  The  maximum 
torques  which  the  shafts  will  withstand  also  are  slightly  greater 
in  the  case  of  the  fluted  shafts  than  in  that  of  the  corresponding 
plain  shafts.  It  was  found  from  these  tests  that  a  fluted  shaft  of 
diameter  d  is  equal  to  a  plain  shaft  of  diameter  0.86d,  as  far  as 
the  elastic  limit  is  concerned. 

Similar  tests  were  made  with  two  sets  of  fluted  shafts  of  nickel 
steel,  of  the  dimensions  shown  in  Fig.  133.  One  of  each  pair  was 
tested  in  the  condition  (except  for  the  machining)  in  which  it  was 
delivered  from  the  forge,  while  the  other  was  oil  hardened  before 
machining  and  testing.  The  results  of  these  tests  are  given  in  the 
following  table : 

TABLE  VIII.— TORSION  TESTS  OF  NICKEL  STEEL  SHAFTS. 


Treatment 

of 
Material 

Normal   .......  2$ 

Oil  Hardened. . 

Normal   Hi 

Oil  Hardened.. 

Normal    If 

Oil  Hardened.. 

Normal    li 

Oil  Hardened 

The  most  remarkable  result  of  Mr.  Larard's  test  is  perhaps  the 
low  elastic  limit  of  mild  steel  as  compared  with  the  breaking 
strength.  It  will  be  seen  from  Table  VIII  that  oil  hardening  sub- 
stantially doubled  the  elastic  limit. 


Diameter  of       Particulars  of       Limit  of 
Specimen.              Keyway.           Elasticity 
Out-      Bottom  of              Depth  at           in 

Torque  at 
Fracture 
in 

side, 
Ins. 

Keyway, 
Ins. 

Width,    Edge, 
Ins.         Ins. 

Pounds- 
Inches. 

Pounds  - 
Inches. 

2* 

2 

i 

& 

41,800 

226,200 

21 

2 

i 

£ 

78,100 

265,200 

Hi 

HI 

A 

ft 

23,000 

107,200 

Iff 

Hi- 

& 

& 

39,600 

116,000 

If 

ll 

H 

4 

11,800 

68,000 

If 

It 

U 

* 

26,800 

77,000 

li 

1 

\ 

i 

5,900 

30,360 

li 

1 

i 

i 

12,200 

33,400 

BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


213 


In  calculating  the  diameter  of  the  shafts  a  stress  of  20,000 
pounds  per  square  inch  may  be  allowed  in  the  case  of  heat 
treated  carbon  steel,  30,000  pounds  per  square  inch  in  the  case 
of  heat  treated  nickel  steel,  and  stresses  proportional  to  their  re- 
spective elastic  limits  in  the  cases  of  other  steels.  The  conven- 
tional formula  for  the  torsional  strength  of  cylindrical  shafts  is 

T  X  12  =  0.196  d?S, 

and  since  a  squared  shaft  is  only  0.7  times  as  strong,  and  the 
maximum  safe  stress  for  carbon  steel  is  20,000  pounds  per  square 
inch,  we  find  the  maximum  safe  load  to  be 

T  X  12  =  0.7  X  0.196  X  20,000  X  d* 
Hence,  for  a  carbon  steel  shaft  with  square  ends 


d  = 


6.12 


Similarly,  for  a  carbon  steel  shaft  with  fluted  or  hexagonal  ends 
^~T~  ,M 

d  = ; 

6.53 

for  a  nickel  steel  shaft  with 
square  ends 


d  = 


6.94 

for  a  nickel  steel  shaft  with 
fluted  or  hexagonal  ends 


for  a  carbon  steel  shaft  with 
upset  ends 


FIG.     134. — DIAGRAM     OF     BENDING 
MOMENT  IN  SEMI-FLOATING  AXLE. 


for  a  nickel  steel  shaft  with  upset  ends 


d  =- 


7.8 

Shafts  of  Semi-Floating  Axles. — In  a  semi-floating  axle 
the  shafts  are  subjected  not  only  to  torsional  loads,  but  also  to  a 
bending  moment.  The  length  of  the  lever  arm  (Fig.  134)  is 
equal  to  the  distance  between  the  centre  plane  of  the  road  wheel 
and  the  centre  line  of  the  outboard  axle  bearing,  and  the  load 
is  equal  to  the  weight  supported  by  one  of  the  rear  wheels.  The 


214          BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

load  on  the  rear  axle  is  not  known  when  a  car  is  designed,  but 
can  be  determined  approximately  by  means  of  the  following 
formulas : 

Two  passenger  runabout 

wheel  base2 

W  = +  200  pounds. 

10 

Five  passenger  open  touring  car 
wheel  base2 

W  = +  600  pounds. 

8 

Seven  passenger  open  touring  car 
wheel  base2 

W  = +  800  pounds. 

9 

The  maximum  bending  moment  on  the  shaft  occurs  at  the 
centre  of  the  bearing  and  is  equal  to  wl,  where  w  is  the  load 
carried  by  one  of  the  wheels,  and  /  the  distance  between  the 
centre  plane  of  the  wheel  and  the  centre  of  the  bearing.  Let  T 
equal  the  maximum  torque  on  one  of  the  axle  shafts  in  pounds- 
feet;  that  is,  one-half  the  product  of  the  maximum  engine  torque 
by  the  low  gear  reduction  ratio  and  the  bevel  gear  reduction 
ratio.  If  the  diameter  of  the  shaft  is  d,  the  distance  c  of  the 

d 

outermost  fibre  from  the  neutral  axis  is  —  and  the  moment  of 

2 

inertia  /  of  the  cross  section  is  ,  hence  inserting  in  the  well 

64 
known  formula  for  bending  stress 

Me 


we  have 


The  polar  moment  of  inertia  of  the  circular  section  is  -  , 
and  inserting  in  the  formula  for  torsional  stress  32 

Me 

St=~T' 

we  get  192  T 

ird5 

These  two  stresses  can  be  combined  by  means  of  the  equation 
given  on  page  172,  as  follows  : 

16  wl  /  192  TV        1    /32W/V 

I 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  215 

Hence 


(61.14  7T  +  --  (10.18  wlY 
d=      ! (45) 

s 

This  diameter  is  required  at  the  bearing.  The  bending  moment 
decreases  uniformly  from  the  centre  of  the  bearing  to  the  centre 
of  the  road  wheel  and  the  centre  of  the  master  gear  hub,  re- 
spectively, and  if  the  lightest  possible  construction  is  desired 
the  shaft  diameter  may  be  decreased  from  the  value  calculated 
by  equation  (45)  at  the  bearing  to  the  diameter  required  for 
the  torsional  stresses  only  at  the  centre  of  the  road  wheel  and 
the  master  gear,  respectively. 

Helical  Bevel  Gears. — There  are  two  types  of  bevel  gears 
employed  in  rear  axle  drives,  viz.,  the  ordinary  bevel  gear  whose 
tooth  elements  are  straight  lines,  and  the  helical  bevel  gear  whose 
tooth  elements  curve  around  the  gear  cone. 

The  helical-bevel  gear  type  of  final  drive  was  introduced 
in  1913  by  the  Packard  Motor  Car  Company,  and  this  drive  has 
since  been  widely  adopted  for  pleasure  cars.  Helical  bevel 
gears  with  gear  axes  at  right  angles  bear  the  same  relation  to 
straight  bevel  gears  as  helical  spur  gears  with  parallel  axes  to 
straight  spur  gears.  Their  chief  advantage  is  their  noiseless 
operation  at  all  speeds,  but  they  have  a  number  of  other  impor- 
tant advantages  which  together  were  responsible  for  their  al- 
most instant  popularity.  These  advantages  are  more  or  less 
inter-related.  For  instance,  with  helical  bevel  gearing  a  smaller 
minimum  number  of  teeth  can  be  used  than  with  straight  bevel 
gearing.  What  limits  the  minimum  number  of  pinion  teeth  in 
straight  bevel  gearing  is  the  fact  that  as  the  number  of  teeth  is 
decreased  the  non-uniformity  of  motion,  and  consequently  the 
noise,  increases.  But  helical  bevel  gearing  is  inherently  far 
more  silent,  hence  this  limitation  is  practically  eliminated  and 
pinions  with  a  smaller  number  of  teeth  may  be  used. 

Cause  of  Non-Uniform  Gear  Motion. — Before  proceeding 
with  the  helical  bevel  gear,  it  will  be  well  to  consider  the  cause 
of  non-uniform  motion  and  noise  in  straight  bevel  and  spur 
gears,  because  it  is  the  absence  of  this  cause  in  the  helical  gear 
to  which  it  owes  its  valuable  properties.  In  a  correctly  cut 
pair  of  involute  spur  gears  there  is — assuming  proper  spacing  of 
shafts  and  absolute  rigidity  of  same — uniform  transmission  of 
motion  as  long  as  the  arc  of  contact  or  arc  of  action  is  not  less 
than  the  circular  pitch.  As  the  number  of  teeth  decreases  the 


216  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

arc  of  contact  approaches  the  circular  pitch  and  with  the  15 
degree  involute  system  12  is  the  smallest  number  of  teeth  with 
which  the  arc  of  contact  exceeds  the  circular  pitch  and  with 
which  uniform  transmission  of  motion  is  theoretically  obtain- 
able. 

The  above  applies  to  perfectly  cut  teeth  while  they  are  new. 
Spur  gear  teeth  have  a  combined  rolling  and  sliding  motion 
and  they  are  naturally  subject  to  wear,  the  wear  on  any  part 
of  the  tooth  flank  being  substantially  proportional  to  the  rela- 
tive sliding  motion  at  that  part  of  the  flank  and  to  the  load 
supported  by  it.  Now,  unfortunately,  the  relative  sliding  mo- 
tion, and,  consequently  the  wear,  varies  greatly  at  different 
points  of  the  tooth  flank. 

Referring  to  Fig.  135,  in  which  two  teeth  of  a  pair  of  meshed 
gears  are  shown  to  be  in  contact  at  the  pitch  points — the  points 
of  intersection  of  the  flanks  with  the  pitch  circles — the  mo- 
mentary direction  of  motion  of  the  contacting  points  of  both 
wheels  is  the  same,  tangential  to  the  pitch  circles  at  their  point 
of  contact.  Hence,  there  is  at  this  moment  no  sliding  of  one 


FIG.   135. — SHOWING  DIRECTION  AND  MAGNITUDE  OF  MOTION  OF 

TOOTH  CONTACT  SURFACES  AT  DIFFERENT  POINTS  OF  MESH. 
tooth  over  the  other,  the  motion  being  purely  rolling.  Now 
consider  the  other  pair  of  teeth  shown  in  contact  in  the  same 
figure.  The  motion  of  each  point  is  in  the  direction  of  a  tangent 
to  a  circle  through  this  point  concentric  with  the  corresponding 
pitch  circle.  These  lines  diverge  considerably,  and  it  is  obvi- 
ous that  when  two  surfaces  in  contact  move  in  different  direc- 
tions they  must  slide  over  each  other.  In  our  example  the 
sliding  motion  is  represented  by  the  dotted  line  connecting 
the  ends  of  the  arrows  representing  the  motion  of  each  point. 
Sliding  in  spur  gears  has  been  investigated  by  O.  Lasche,  and 
Fig.  136  represents  his  wear  characteristic  showing  the  distribu- 
tion of  wear  over  the  tooth  flank.  There  is  no  sliding  at  the 
pitch  line,  and  wear  increases  from  the  pitch  line  both  toward 
the  top  and  the  root  of  the  tooth.  This  effect  can  often  be 
plainly  seen  on  an  old  straight  spur  or  bevel  gear  on  which 
there  is  a  line  on  the  tooth  flank  at  pitch  height  which  does  not 
show  any  wear  while  all  the  rest  of  the  flank  is  polished. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  217 

When  a  tooth  flank  is  thus  unevenly  worn,  the  condition  of 
uniform  motion — that  a  normal  to  the  contact  surfaces  must 
always  pass  through  the  pitch  point — is  no  longer  fulfilled.  The 
result  is  that  the  gears  transmit  motion  non-uniformly,  the 
driven  gear  is  alternately  accelerated  and  allowed  to  decelerate, 
and,  in  consequence,  the  gear  is  noisy.  True  helical  bevel  gears 
are  gears  cut  from  blanks  of  frustrated  conical  form,  the  teeth 
of  which  curve  around  the  gear  axis  in  such  a  way  that  the 
elements  of  the  tooth  in  the  pitch  cone  surface  always  make  the 
same  angle  with  a  pitch  surface  element.  This  angle  is  known 
as  the  angle  of  spiral.  In  practice  the  elements  of  the  teeth 
form  circular  arcs  of  given  radius  and  the  gear  approximates 
the  true  helical  bevel  form. 


Arc  of  Approach  Arc  of  Recess 

FIG.  136.— WEAR  CHARACTERISTIC  OF  GEAR  TOOTH. 

Helical  bevel  gears  may  be  either  right  hand  or  left  hand, 
according  to  the  direction  in  which  the  teeth  wind  around  the 
gear.  Only  gears  of  unlike  denomination  will  mesh  together, 
that  is,  a  right  hand  pinion  with  a  left  hand  gear,  or  a  left 
hand  pinion  with  a  right  hand  gear.  The  question  of  whether 
to  use  right  hand  or  left  hand  pinions  is  of  much  importance, 
as  the  denomination  of  the  pinion  determines  the  direction  and 
magnitude  of  the  end  thrust,  which  is  much  greater  with  helical 
bevel  than  with  ordinary  bevel  gears. 

Angle  of  Spiral. — In  laying  out  a  pair  of  helical  bevel  gears 
one  of  the  factors  to  decide  on  is  the  angle  of  spiral.  This 


218  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

should  be  such  that  the  angular  advance  corresponding  to  the 
face  length  of  the  gear  is  somewhat  greater  than  the  circular 
pitch.  If  this  relation  holds,  then  there  is  at  all  times  pitch 
line  contact  at  some  part  of  the  teeth  and  this  obviates  any 
tendency  of  the  gear  teeth  to  wear  away  more  quickly  on  some 
part  of  their  flanks  than  on  others;  for,  as  soon  as  any  part 
of  the  flank  wore  ever  so  little  more  than  the  pitch  line,  the 
pressure  at  that  part  would  be  reduced  and  the  wear  thereby 
automatically  cut  down.  This  is  the  principle  which  insures 
that  tooth  contact  in  a  helical  bevel  gear  does  not  deteriorate 
with  age  and  that  such  a  gear  remains  quiet  throughout  its 
life. 

Minimum  Number  of  Teeth. — High  speed  motors,  espe- 
cially those  of  moderately  powered  cars,  require  a  high  gear  re- 
duction and  the  helical  bevel  gear  has  made  it  possible  to  obtain 
this  higher  reduction  in  a  single  step  without  running  the  risk 
of  non-uniform  and  noisy  tooth  action. 

Helical  bevel  drives  with  pinions  of  ten  teeth  are  entirely 
practical  and  these  permit  of  obtaining  any  gear  ratio  that 
may  be  needed  for  pleasure  cars.  In  the  case  of  such  small 
numbers  of  teeth  the  pinion  must  be  made  integral  with  its 
shaft.  As  regards  strength  it  is  believed  that  a  helical  bevel 
pinion  of  a  given  pitch  diameter  and  cut  with  teeth  of  a  certain 
diametral  pitch  will  safely  transmit  the  same  power  at  a  certain 
speed  as  a  straight  bevel  pinion  with  the  same  pitch  diameter 
and  diametral  pitch;  this  notwithstanding  the  fact  that  the 
normal  load  on  the  teeth  is  considerably  greater  than  with  the 
straight  bevel  gear.  If  the  power  transmitted  is  the  same  the 
tangential  force  will  be  the  same  in  the  two  cases.  On  the 
other  hand  the  end  thrust  is  much  greater  with  the  helical 
than  the  straight  pinion  and  the  normal  tooth  load  usually 
figures  out  about  15  per  cent  higher  in  the  case  of  the  former. 
Probably  the  chief  reason  for  the  greater  strength  of  the  helical 
pinion  is  that  since  there  is  always  pitch  line  contact  there 
can  be  no  non-uniform  motion  to  cause  heavy  extra  strains. 
There  is,  however,  another  reason  for  the  greater  strength  of 
a  helical  bevel  pinion,  and  that  is  that  it  has  more  teeth  in 
contact  at  one  time.  If  the  spiral  advance  corresponding  to 
the  width  of  face  is  greater  than  the  circular  pitch,  then  the 
arc  of  action  includes  always  at  least  one  more  tooth,  than  in  a 
similar  straight  bevel  set.  The  two  outer  teeth  will  be  in  con- 
tact over  only  a  part  of  their  length,  but  as  far  as  breakage  is 
concerned  practically  their  whole  strength  counts. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  219 

In  practice  the  angle  of  spiral  is  usually  30  degrees  or  close 
to  it,  as  with  the  pitches  and  proportions  of  face  width  to 
centre  distance  this  gives  a  spiral  advance  somewhat  greater  than 
the  circular  pitch. 

Since  the  circular  pitch 


P* 
and  the  spiral  advance 

s  =  f  sin  0 

where  PA  is  the  diametral  pitch;  /,  the  face  width  and  0,  the 
angle  of  spiral,  we  have  in  the  case  of  a  50  tooth  5  diametral 
pitch  gear  with  30  degree  angle  of  spiral  and  1^-inch  face, 

3.146 
PA  =  -  =  0.628  inch 

s  =  1.5  X  0.5  =  0.75  inch 

which  gives  an  overlap  of  about  20  per  cent.  For  unusually 
small  pitches  or  relatively  large  face  widths  smaller  angles  of 
spiral  will  give  the  necessary  overlap  of  teeth,  and  with  the 
reverse  conditions  a  greater  angle  of  spiral  must  be  used,  but 
makers  of  gear  cutting  machinery  advise  against  an  angle  larger 
than  35  degrees. 

Calculation  of  Blanks.  —  The  calculation  of  the  blanks  for 
the  pinions  and  gears  partakes  of  the  methods  used  for  calculat- 
ing the  blanks  for  straight  bevel  gears  and  helical  spur  gears 
respectively.  Thus,  for  instance,  the  pitch  diameter  is  calculated 
by  the  same  equation  as  used  in  the  case  of  helical  spur  gears, 
viz.,  N 


pn  X  cos  a 

where  N  is  the  number  of  teeth  ;  />n,  the  normal  diametral  pitch 
and  a  the  angle  which  the  tooth  flank  element  makes  with  the 
pitch  cone  element  (angle  of  spiral).  With  regard  to  the  adden- 
dum there  is  no  complete  agreement.  In  spur  gears  the  ad- 
dendum is  made  equal  to  0.3183  pc  =  I/pa,  and  the  dedendum, 
0.3683  />c  =  1.157//M,  the  latter  being  the  sum  of  a  working 
depth  of  0.3183  pc  below  the  pitch  circle  and  a  clearance  of 
0.05  pc  =  0.157//>d.  Therefore,  the  total  working  depth  of 
0.6866  pc  =  2//>d  extends  equally  above  and  below  the  pitch 
circle.  Now  it  is  known  that  in  a  pinion  with  a  small  number 
of  teeth  there  is  a  tendency  to  undercutting  and  consequent 
weakening  of  the  pinion  teeth.  To  obviate  this  it  is  customary 
in  helical  bevel  pinions  to  have  most  of  the  working  depth 


220          BEVEL  GEAR  DRIVE  AND  REAR  AXLE 

above  the  pitch  circle.  One  maker  of  helical  bevel  gear  cutting 
machines  recommends  that  on  the  pinion  0.7  of  the  working 
depth  be  above  the  pitch  circle  and  0.3  below  the  pitch  circle. 
In  the  gear  the  proportion  must  be  reversed,  that  is,  0.3  of  the 
working  depth  must  be  above  the  pitch  circle  and  0.7  below  the 
pitch  circle. 

Let  it  be  required  to  lay  off  the  blanks  for  a  helical  bevel 
gear  and  pinion  of  48  and  12  teeth  respectively,  5  pitch,  30  de- 
gree angle  of  spiral  with  0.7  of  the  working  depth  above  and  0.3 
below  the  pitch  circle  in  the  pinion.  We  have  in  the  first  place 
for  the  maximum  pitch  diameters 
12 

=  2.771  inches 

5  X  0.866 
and 

48 
=  11.085  inches. 


5  X  0.866 

The  total  working  depth  of  the  5  pitch  teeth  is 
2 

—  =  0.4  inch 
5 

hence,  in  the  pinion  the  working  depth  above  the  pitch  circle 
or  the  addendum  is 

0.7  X  0.4  =  0.28  inch 
and  the  working  depth  below  the  pitch  circle 

0.3  X  0.4  =  0.12  inch. 
The  clearance  is  0157 

— =  0.0314  inch. 

5 

The  pitch  angle  of  the  pinion  is  such  that 

2.771 

tangent  pitch  angle  = =  0.25 

11.085 

pitch  angle  =  14  degrees. 

The  face  angle  of  the  pinion  is  greater  than  the  pitch  angle  by 
an  angle  such  that  its  tangent  is 
0.28 

=  0.0487 

V1.3852  +  5.S432 
and  the  angle  is  2°  47'. 
Hence,  the  face  angle  is  16°  47'. 
The  face  diameter  of  the  pinion  is 

2.771  +  (2  X  0.28  X  cos  14°)  =  3.314. 

The  pitch  angle  of  the  gear  is  the  complement  of  the  pitch  angle 
of  the  pinion  or 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE 


221 


90°  _  14°  =  76° 

and  the  angle  which  the  addendum  adds  to  the  pitch  angle  is 
such  that  its  tangent  is 

0.12 

=  0.0208 

V1.3852  +  5.543s 


FIG.  137.— LAY-OUT  OF  A  PAIR  OF  HELICAL  BEVEL  GEARS. 


and  the  angle  is  1°  12', 
hence,  the  face  angle  is 

76°  +  1°  12'  =  77°  12' 


222  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

Strength  of  Bevel  Gears.  —  As  was  stated  previously,  a  pair 
of  helical  bevel  gears  of  given  pitch  diameters  and  pitch  will 
transmit  the  same  power  as  a  pair  of  straight  bevel  gears  of 
the  same  pitch  diameters  and  pitch,  and  the  following  consid- 
eration applies  to  both  kinds  of  gears.  A  modification  of  the 
Lewis  formula  has  been  worked  out  for  bevel  wheels,  according 
to  which  the  strength  of  a  bevel  pinion  is  equal  to  that  of  a  spur 
pinion  of  the  same  face,  pitch  and  number  of  teeth,  multiplied 
by  the  ratio  of  the  smallest  to  the  largest  pitch  diameter.  It 
is  at  once  apparent  that  this  formula  is  not  a  rational  one,  for 
if  the  pinion  face  extended  nearly  to  the  apex  the  formula 
would  make  the  strength  almost  nil,  which  is  far  from  being 
correct.  It  is  therefore  stipulated  that  the  formula  shall  be 
applied  only  if  the  small  pitch  diameter  is  not  less  than  two- 
thirds  the  big  pitch  diameter.  But  if  this  formula  is  applied 
to  existing  automobile  bevel  gears  it  is  found  to  give  such 
high  values  for  the  stress  that  it  is  at  once  seen  to  be  incorrect. 
The  trouble  is  mainly  with  the  Lewis  formula,  which  is  based  on 
wrong  assumptions.  Instead  of  the  whole  tangential  force  com- 
ing at  the  end  of  one  tooth,  the  force  is  always  divided  between 
two  or  more  teeth,  and  when  the  contact  is  at  the  end  of  one 
tooth  it  is  not  at  the  end  of  the  other  tooth  or  teeth.  G.  H. 
Marks,  who  made  a  series  of  tests  on  cut  gears  at  Leland  Stan- 
ford, Jr.,  University,  which  were  reported  in  a  paper  read  before 
the  American  Society  of  Mechanical  Engineers  in  1912,  showed 
that  the  Lewis  formula  is  partly  based  on  erroneous  premises 
and  that  the  arc  of  action  must  be  taken  into  account  to  get  a 
tolerably  accurate  result  if  gears  of  all  kinds  are  considered. 

The  bevel  gear  tooth,  whether  straight  or  helical,  decreases 
in  pitch  uniformly  from  the  outer  end,  where  the  pitch  has 
the  nominal  value,  to  the  apex  of  the  gear  cone.  Let  the  face 
width  be  equal  to  1  —  <*  per  cent  of  the  distance  from  the 
outer  end  of  the  tooth  to  the  apex,  which  distance  we  may  desig- 
nate by  L.  Now  let  us  take  any  small  section  dx  of  the  tooth 
at  a  distance  x  from  the  apex.  The  tangential  pressure  which 
this  section  will  support  we  know  to  be  proportional  to  the 
circular  pitch  and  to  the  width  of  face  dx.  But  the  circular 
pitch  at  this  part  of  the  face  width,  if  p  is  the  nominal  circular 
pitch,  is 

x 


Also,  a  tangential  force  Fx  on  the  pitch  circle  at  a  distance  x 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  223 

from  the  apex  is  equivalent  to  a  tangential  force  on  the  maxi- 
mum pitch  circle 

x 

X  L 

Hence    we    may    write    for    the    tangential    force    which    the 
section  dx  of  the  tooth  will  support  (using  the  Lewis  formula) 
x  Spy 

L  L 

and  this  is  equivalent  to  a  tangential  force  on  the  pitch  circle 
of  the  large  end  of 

Spy  x       Spy 

d  F  _ x2dx  X  —  = x2  dx 

L  L          L- 

If  we  integrate  this  expression  between  the  limits  x  =  L  and 
x  =  a  L  we  get 

f  L 

I   Spy  Spy   /L3         a8L8  \ 

F  =        x2dx  = ( ) 

I      L2  L2      \3  3      / 

JaL 

SLpy   /  \ 

=  -^-(1-aS) (46) 

in  which  F  is  the  tangential  force  on  the  pitch  circle  at  the 
large  end;  S,  the  permissible  stress  in  pounds  per  square 
inch ;  p,  the  circular  pitch  at  the  large  end ;  L,  the  pitch  line 
length  from  the  large  end  of  the  pinion;  y,  the  Lewis  con- 
stant for  the  particular  number  of  teeth,  and  a,  the  proportion 
of  the  pitch  line  length  from  the  inner  end  of  the  pinion  to 
the  apex,  to  the  pitch  line  length  from  the  outer  end  of  the 
pinion  to  the  apex  of  the  cone.  To  be  absolutely  correct  the 
equation  should  also  contain  a  factor  depending  upon  the  num- 
ber of  teeth  in  contact  at  one  time  and  a  factor  dependent  upon 
the  pitch  line  velocity.  But  both  of  these  items  vary  only 
within  relatively  narrow  limits  in  pleasure  cars,  and  as  there  is 
some  uncertainty  as  to  their  exact  influence  on  the  strength  of 
the  gears  it  is  permissible  to  neglect  them.  Practical  data  in 
the  author's  possession  shows  that  if  a  heat  treated  alloy  steel, 
such  as  3l/>  per  cent  nickel  or  its  equivalent,  is  used,  the  value 
of  the  stress  in  the  above  equation  may  be  25,000.  This 
stress  has  been  arrived  at  by  analyzing  the  gears  of  several 
rather  high  powered  cars  and  is  based  on  the  direct  torque  of 
the  engine,  not  the  geared-up  torque.  It  appears  that  in  mod- 
erately powered  cars  in  which  the  full  engine  power  is  used  a 


224          BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

greater  part  of  the  time  and  where  space  restrictions  are  not 
so  severe,  the  gears  are  made  somewhat  more  liberal  and  a 
stress  of  20,000  may  be  used.  Also,  if  the  material  is  not 
equivalent  to  3l/2  per  cent  nickel  steel,  the  stress  should  be  chosen 
lower  in  proportion  to  the  elastic  limits.  Using  a  somewhat 
lower  stress,  which  leads  to  gears  of  larger  dimensions,  has  the 
advantage,  at  least  in  the  case  of  straight  bevel  gears,  that,  ow- 
ing to  the  larger  contact  surfaces  the  tendency  to  noisy  operation 
is  reduced. 

Direction  of  Thrust  Loads. — When  a  car  is  being  driven  for- 
ward, the  propeller  shaft  and  bevel  pinion  turn  right-handedly, 
while  when  the  car  is  being  backed  the  bevel  pinion  turns  left- 
handedly.  Therefore,  a  right-hand  pinion  tends  to  draw  into 
the  gear  when  the  car  is  being  driven  forward,  as  a  result  of 
the  curvature  of  the  teeth.  The  other  causes  of  end  thrust, 
viz.,  the  taper  of  the  pinion  cone  and  the  pressure  angle,  tend 
to  force  the  pinion  out  of  the  gear.  Of  these  two  forces  the 
former  is  always  the  greater,  and  the  net  end  thrust  on  the 
shaft  of  a  right-hand  pinion  is  in  the  direction  toward  the  gear 
center  and  equal  to  the  difference  between  the  end  thrust  due 
to  the  curvature  of  the  teeth  on  the  one  hand  and  that  due  to 
the  pinion  cone  angle  and  the  pressure  angle  on  the  other. 

In  backing,  the  end  thrust  due  to  the  curvature  of  the  teeth 
of  a  right-hand  helical  pinion  is  away  from  the  gear  center  and 
in  the  same  direction  as  the  end  thrust  due  to  the  cone  angle 
and  pressure  angle.  The  resultant  is,  therefore,  in  the  direc- 
tion away  from  the  gear  center  and  equal  to  the  sum  of  the 
end  thrusts  due  to  tooth  curvature,  cone  angle  and  pressure 
angle,  respectively.  Evidently,  therefore,  with  a  right-hand 
pinion  the  end  thrust  is  a  maximum  when  the  car  is  being 
backed. 

With  a  left-hand  pinion  all  end  thrusts  add  together  for  for- 
ward drive  and  are  in  the  direction  away  from  the  center  of 
the 'gear,  while  for  the  reverse  drive  the  end  thrust,  though 
still  in  the  same  direction,  is  equal  in  amount  to  the  difference 
between  that  due  to  tooth  curvature  on  the  one  hand  and  to 
the  cone  angle  and  pressure  angle  on  the  other.  The  maximum 
end  thrusts  are  the  same  whether  a  right  or  left-hand  pinion 
is  used.  As  the  car  is  being  driven  forward  most  of  the  time, 
the  right-hand  pinion  seems  to  have  the  advantage,  but  some 
designers  prefer  the  left-hand  pinion  because  heavy  thrust  loads 
in  the  direction  away  from  the  gear  center  can  be  accommodated 
more  readily  than  those  in  the  opposite  direction. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


225 


Center  of  Load  Distribution. — In  attempting  to  calculate  the 
thrust  loads  we  must  first  determine  the  center  of  load  distri- 
bution on  a  pinion  tooth.  We  will  assume  that  the  load  is  dis- 
tributed along  the  tooth  in  proportion  to  the  strength  of  the 
tooth  section,  which  is  an  ideal  condition.  In  actual  practice 
the  adjustment  of  the  gears  will,  of  course,  have  much  to  do 
with  the  load  distribution.  Let  n  be  the  ratio  of  the  tooth  face 
to  the  pitch  line  length  from  the  large  end  of  the  tooth  to  the 
pitch  cone  apex,  and  let  m  be  the  proportion  of  the  pitch  line 
length  represented  by  the  distance  from  the  apex  to  the  center 
of  the  tooth  load.  From  the  well-known  formula  for  strength 
of  gears  it  is  known  that  the  strength  of  a  tooth  section  is 
directly  proportional  to  the  circular  pitch  at  that  section,  and 
the  pitch,  of  course,  decreases  uniformly  from  the  large  end 
of  the  tooth  to  the  apex,  where  it  is  zero.  The  strength  of  a 
section  of  the  bevel  gear  is  also  proportional  to  the  width  of 
that  section.  In  Fig.  138  the  vertical  lines  ab,  cd  and  ef  repre- 


FIG.  138. — LOCATING  CENTER  OF  DISTRIBUTION  OF  TOOTH  LOAD. 

sent  the  circular  pitch  at  the  respective  points  and  the  line  cd 
is  supposed  to  divide  the  entire  gear  into  two  parts  of  equal 
strength.  As  the  strength  .  of  a  gear  is  proportional  to  the 
product  of  its  circular  pitch  into  its  width  of  face,  the  two 
areas  A  and  B  should  be  equal.  If  this  is  the  case,  then 

[Lsin*+.L  (l-n)sin 
|  n  L  cos  5 


'L  sin  5  +  m  L  sin  5 


—  mL)  cos8X2 


+  L(1  — n) 


nL=  (L  +  mL)  (L  — nL) 


2L  —  nL 


n  L 


—  m2  L2 


226  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

n*  L2 


n 


=  L2  —  m2  L2 


n =  1  —  w2 

2 


Multiplying  the  pitch  diameter  by  this  value  m  we  get  the 
effective  pitch  diameter,  and  with  the  aid  of  this  we  get  the 
tangential  effort  on  the  corresponding  pitch  circle  by  means  of 
the  equation 

TX24 


FIG.  139.— SHOWING  RELATION  BETWEEN  TANGENTIAL  FORCE 
AND  NORMAL  TOOTH  PRESSURE. 

The  normal  load  on  the  tooth  contact  surface  is,  of  course, 
considerably  greater  than  the  tangential  force,  owing  to  the 
inclination  of  the  tooth  elements  against  the  pitch  cone  elements 
(angle  of  spiral)  on  the  one  hand,  and  to  the  inclination  of  the 
tooth  flank  (pressure  angle)  on  the  other.  If  we  designate  the 
angle  of  spiral  by  a  and  the  pressure  angle  of  the  tooth  by  P, 
the  normal  pressure  on  the  tooth  is 

F 
P  =  

co s  cc  co s  P 

as  may  be  readily  seen  from  Fig.  139  in  which  AB  represents 
the   tangential    force  on   the  pinion,   AC  the   force   in   a   plane 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


\      I 


FIG.  140. — SHOWING  RELATION  BETWEEN  TANGENTIAL  FORCE  AND 
PRESSURE  ALONG  PITCH  CONE  ELEMENT. 

tangent  to  the  pitch  cone  and  perpendicular  to  the  tooth  ele- 
ment, and  CD  the  force  normal  to  the  contact  surfaces.  While 
in  determining  the  bearing  loads  of  straight  spur  and  bevel 
gears  a  friction  angle  of  5  degrees  is  generally  figured  with, 
this  does  not  seem  necessary  in  the  case  of  helical  gears,  as 
there  is  always  pitch  line  contact  at  some  point,  and,  conse- 
quently, pure  rolling  motion  at  this  point,  with  very  little  slid- 
ing motion  on  the  whole.  The  problem  now  is  to  resolve  the 
pressure  P  into  a  component  parallel  to  the  pinion  axis  (thrust 
load)  and  another  component  perpendicular  to  the  pinion  axis 
(radial  load). 

We  first  find  the  components  of  the  tooth  pressure  along  an 
element  of  the  pitch   cone   and  perpendicular  to   that  element, 


FIG.   141.— PRESSURE  ALONG  PITCH   CONE  ELEMENT  RESOLVED 
INTO  AXIAL  AND  RADIAL  COMPONENTS. 


228 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


respectively.  In  Fig.  140  is  shown  a  plan  view  of  a  right-hand 
pinion  supposed  to  rotate  right-handedly.  The  horizontal  arrow 
represents  the  tangential  force  F  on  the  inclined  tooth  and  the 
vertical  arrow  the  resulting  pressure  along  the  pitch  cone  ele- 
ment. It  will  be  seen  that 

'Ce 

=  tan  cc,  hence  Ce  =  F  tan  a 

F 

This  pressure  along  the  pitch  cone  element  can  again  be  re- 
solved into  two  components,  as  shown  in  Fig.  141,  one  parallel  to 
the  pinion  axis  and  the  other  perpendicular  thereto.  It  is  here 
necessary  to  take  account  of  the  direction  of  the  forces  and  we 
will  call  axial  forces  in  the  direction  from  the  small  to  the 


FIG.   142. — COMPONENTS   OF   NORMAL   TOOTH   PRESSURE   PERPEN- 
DICULAR TO  PITCH  CONE  ELEMENT. 

large  end  of  the  pinion,  or  away  from  the  apex  of  the  cone, 
positive,  and  those  in  the  opposite  direction,  negative.  Radial 
forces  from  the  point  of  contact  toward  the  axis  will  be  called 
positive  and  those  oppositely  directed,  negative. 

Resolving  the  force  along  the  pitch  cone  element  we  get  for 
the  axial  component 

Ca  =  —  F  tan  cc  cos  8 
and  for  the  radial  component 

CT  =  F  tan  cc  sin  5. 

We  next  take  up  the  component  of  the  normal  tooth  pressure 
perpendicular  to  the  pitch  cone  element  through  the  point  of 
contact.  From  Fig.  142  it  can  be  seen  that  this  component  Cp 
is  equal  to 

F  sin  j3                 tan  ft 
p  sin  ft  = =  F • 


cos  cc  cos  /3 


cosv 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE 


229 


This  component  perpendicular  to  the  pitch  cone  element  also 
may  be  further  resolved  into  axial  and  radial  components,  as 
illustrated  in  Fig.  143,  the  axial  component  being 

tan  /3  sin  8 
C«a  =  F 


and  the  radial  component 


COS  Ct. 

tan  8  cos  8 


FIG.  143.  — COM- 
PONENT PERPEN- 
DICULAR TO  PITCH 
CONE  ELEMENT 
RESOLVED  INTO 
AXIAL  AND  RA- 
DIAL C  o  M  P  o  - 

NENTS. 


cos  a. 

We  now  add  like  components  of  the  forces 
along  the  pitch  cone  element  and  perpen- 
dicular to  that  element  respectively  and  ob- 
tain for  the  end  thrust  on  a  right-hand  heli- 
cal pinion  turning  right-handedly  (forward 
drive) 

tan  8  sin  8  \ 

La  =  F  ( —  tan  oc  cos  8  + I 

cos  a      / 
and  for  the  radial  load  on  such  a  pinion 

tan  8  co s  5  \ 

Lr  =  F  (tan  cc  sin  S  -f- I 

cos  a    I 

These  same  equations  apply  to  the  case  of  a 
left-hand  pinion  turning  left-handedly  (re- 
verse motion).  If  a  left-hand  pinion  turns 
right-handedly  (forward  motion),  the  com- 
ponent along  the  pitch  cone  element  is  in 
the  direction  away  from  the  apex  of  the 
cone  and  the  sign  of  its  axial  component 
becomes  positive.  The  same  applies  to  a 
right-hand  pinion  turning  left-handedly. 
However,  the  radial  component  of  the  force 
acting  along  the  pitch  cone  element  is  in  this 
case  directed  from  the  axis  through  the 
point  of  contact  and  is,  therefore,  negative. 
We,  therefore,  have  for  the  axial  and  radial 
forces  on  a  left-hand  helical  pinion  turning 
right-handedly  (forward  drive)  or  a  right- 
hand  helical  pinion  turning  left-handedly 
(reverse  drive.).  tan  $  sin  8 
La  =  F  (tan  cc  cos  8  +  


and 


F  ( —  tan  cc  sin  8  + 


cos  cc 
tan  8  cos  8 

COSCf. 


230 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE 


Axial  and  Radial  Loads  on  Gear — Since  action  and  reaction 
are  equal  and  opposite,  the  axial  load  or  end  thrust  or*  the  gear 
is  equal  and  opposite  in  direction  to  the  radial  load  on  the  pinion, 
and  the  radial  load  on  the  gear  is  equal  and  opposite  in  direction 
to  the  axial  load  on  the  pinion.  There  is,  therefore,  no  need  of 
separately  calculating  the  gear-bearing  loads.  We  may  summar- 
ize our  equations  as  follows: 


FIG.  144. — GLEASON  AUTOMATIC  HELICAL  BEVEL  GEAR  GENERATING 
MACHINE. 


Right-Hand  Pinion  Turning  Right-Handedly. 

Left-Hand  Pinion  Turning  Left-Handedly. 

End  Thrust  on  Pinion — Radial  Load  on  Gear. 

tan  /3  sin  5  \ 

Li  =  F  ( —  tan  cc  cos  5  + 1 

cos  a.     / 

Radial  Load  on  Pinion,  End  Thrust  on  Gear. 

tan  j3  cos  5  \ 
L2  =  F  (tan  cc  sin  5  + 1 

COSCf.        / 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

Right-Hand  Pinion  Turning  Left-Handcdly. 
Left-Hand  Pinion  Turning  Right-Handedly. 
End  Thrust  on  Pinion,  Radial  Load  on  Gear. 

tan  P  sin  8  \ 

L3  =  F  (tan  a  cos  5  -f  I 

cos  a.     / 

Radial  Load  on  Pinion,  End  Thrust  on  Gear. 

tan  P  cos  5  \ 

£4  =  F  (_  tan  cc  sin  8  +  — —         -  1 

cos  a.      / 


231 


FIG.  145.— CUTTER  FOR  FINISHING  HELICAL  BEVEL  GEARS. 


in  which 

F  is  the  tangential  force  at  the  mean  effective  pitch  radius 
of  the  pinion ;  a,  the  angle  of  spiral ;  p,  the  pressure  angle  of  the 
teeth ;  5,  the  pinion  pitch  angle. 

Manufacture  of  Helical  Bevel  Gears — By  the  Gleason  method 
the  teeth  of  a  helical  bevel  gear  or  pinion  are  cut  by  means  of 
a  revolving  cutter  12  inches  in  diameter  with  twenty  inserted 
blades.  Half  of  the  blades  (alternate  ones)  serve  for  finish- 
ing the  inside  flank  of  the  teeth  and  the  other  half  for  finish- 
ing the  outside  flank.  The  machine  works  on  the  generating 


232  BEVEL  GEAR  DRIVE  AND  REAR  AXLE 

principle,  the  tooth  flank  being  generated  by  relative  motion 
of  the  cutter  holder  and  the  work.  One  side  of  the  tooth  is 
finished  at  a  time,  and  when  all  the  teeth  have  been  finished  on 
one  side  the  setting  of  the  cutter  and  gear  is  changed  before 
work  is  begun  finishing  the  other  side  of  the  teeth.  The  cutter 
carriage  is  mounted  on  a  vertical  column  which  is  supported 
on  a  cradle  with  circular  ways.  A  reversing  mechanism  is 
employed  to  roll  the  cradle  and  rock  the  work.  By  means  of 
compound  change  gears  the  proper  relative  motion  of  the  cradle 
and  work  may  be  secured. 


FIG.  146. — TYPICAL  HELICAL  BEVEL  GEAR  SET. 

One  advantage  of  the  helical  bevel  gear  over  straight  bevel 
gears  is  that  with  the  former  not  nearly  the  same  degree  of 
adjustment  is  required  in  order  to  insure  good  tooth  contact 
and  noiseless  operation. 

Straight  Bevel  Gears — Straight  bevel  gears  can  be  made  with 
six  pitch  teeth  for  pleasure  cars  of  the  very  smallest  size,  say 
those  with  engines  up  to  100  Ibs.-ft.  torque;  five  pitch  for  cars 
with  engines  of  100-200  Ibs.-ft.  torque,  and  four  pitch  for  cars 
with  engines  of  more  than  200  Ibs.-ft.  torque.  The  pinions  are 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE  233 

made  with  from  eleven  to  eighteen  teeth.  In  the  largest  cars  the 
pitch  diameter  of  the  bevel  gear  is  limited  to  about  12  inches, 
and  in  medium  sized  cars  to  11  inches  by  reason  of  the  required 
ground  clearance.  The  capacity  of  straight  bevel  gears  may  be 
found  by  means  of  the  same  equation  (46)  as  for  helical  bevel 
gears,  and  the  thrust  and  radial  bearing  loads  can  be  calculated 
by  the  methods  explained  in  Chapter  III. 

In  extremely  powerful  cars  the  gear  dimensions  have  to  be 
made  somewhat  smaller,  and  in  low  powered  cars  they  can  be 
made  slightly  more  liberal  as  the  lower  unit  pressures  result  in 
greater  silence  of  operation  and  the  wear,  of  course,  is  also 
reduced.  In  America  straight  bevel  gears  are  now  used  only  on 
the  cheaper  pleasure  car  and  on  light  delivery  wagons. 

Axle  Housings — There  are  two  general  types  of  rear  axle 
housings,  viz.,  built-up  housings  consisting  of  a  central  driving 
gear  housing  of  cast  metal  and  of  tubes  forced  into  or  bolted  to 
them,  and  integral  pressed  steel  or  drop  forged  housings.  The 
latter  are  a  comparatively  recent  development,  and  since  they 
possess  important  advantages  in  the  way  of  strength  and  mini- 
mum weight,  they  are  rapidly  coming  into  extensive  use.  We 
will  first  consider  the  older  type,  the  built-up  axle. 

The  central  cast  portion  or  driving  gear  housing,  which  is 
generally  cast  of  either  steel  or  malleable  iron,  and  occasionally 
of  aluminum,  may  be  made  in  different  ways,  as  shown  in 
Fig.  147.  It  must  be  of  such  a  form  as  to  accommodate  the 
differential  and  driving  bevel  gears,  and  it  must  be  either  split 
in  halves  or  provided  with  an  opening  big  enough  to  admit  the 
driven  bevel  gear.  Some  designers  give  this  housing  such  a 
form  that  its  walls  at  every  point  lie  close  to  some  contained 
part,  which  necessarily  leads  to  a  more  or  less  irregular  outside 
shape,  whereas  others  employ  regular  housings  of  bulbous,  spher- 
ical or  cylindrical  shape.  In  order  to  secure  the  necessary 
strength  with  a  minimum  weight  of  material  it  is  often  neces- 
sary to  rib  the  housing.  The  ribs  may  be  placed  either  on  the 
outside  or  on  the  inside,  but  internal  ribbing  has  gained  con- 
siderably in  favor  of  late,  as  a  smooth  outside  form  is  much 
easier  to  keep  clean. 

Formerly  housings  split  substantially  in  halves,  as  shown  at 
A  and  B,  Fig.  147,  were  much  used,  and  both  are  still  met  with. 
It  is  now,  however,  more  common  practice  to  make  the  greater 
part  of  the  case  in  a  single  piece,  with  a  segmental  cover  either 
on  top,  as  at  C,  or  at  an  angle,  as  at  D,  so  the  opening  is  most 
accessible  from  the  rear  of  the  car.  As  stated,  these  large  open- 


234 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE 


ings  primarily  serve  the  purpose  of  introducing  the  bevel  gear 
and  differential.  In  some  designs  of  rear  axle  the  differential 
is  carried  by  a  special  plate  bolted  to  the  front  of  the  driving 
gear  housing,  which  latter  has  large  openings  both  in  front  and 
rear. 

Axle  Tubes—Besides  the  driving  gear  housing  the  supporting 
structure  of  the  built-up  rear  axle  comprises  a  pair  of  so-called 
axle  tubes.  These  are  generally  made  from  drawn  material,  but 
occasionally  they  are  cast.  In  a  semi-floating  axle  the  tubes 
may  be  of  uniform  section  from  end  to  end,  but  in  a  full 


C  D 

FIG.  147. — TYPES  OF  DRIVING  GEAR  HOUSINGS. 


floating  axle  they  are  generally  swaged  down  to  a  smaller 
diameter  where  they  pass  through  the  hubs,  so  that  it  is  not 
necessary  to  use  inordinately  large  bearings  in  the  hubs.  The 
inner  portion  of  the  tubes  should  preferably  be  of  considerable 
diameter,  as  less  weight  of  material  is  then  required  in  order  to 
produce  a  certain  resistance  to  bending  and  torsional  strains. 

The  tubes  may  be  fitted  to  the  driving  gear  housing  in  different 
ways.  Ordinarily  they  are  forced  under  pressure  into  integral 
hubs  of  the  driving  gear  housing  and  are  then  riveted,  as  shown 
in  Fig.  148  at  A.  This  makes  a  very  good  job.  They  may  also 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


235 


be  screwed  into  the  hubs  of  the  housing  and  riveted.  Instead 
of  being  riveted  the  tubes  may  be  secured  by  brazing,  but  this 
is  open  to  the  objection  that  in  brazing  there  is  some  danger  of 
accidentally  overheating  the  metal  and  thus  depriving  it  of  a 
great  deal  of  its  strength.  The  hubs  of  the  housing  should 
preferably  be  beaded  at  their  outer  end.  Some  designers  pro- 
vide flanged  sleeves  which  are  brazed  onto  the  tubes  and  are 
bolted  to  the  driving  gear  housing.  This  makes  it  possible  to 


FIG.  148. — METHODS  OF  SECURING  AXLE  TUBES  TO  DRIVING 
GEAR  HOUSING. 

renew  one  of  the  tubes  at  any  time  without  the  necessity  of 
bringing  it  to  a  well-equipped  machine  shop.  This  construction 
is  illustrated  in  Fig.  148  at  B.  A  very  excellent  though  little 
used  method  consists  in  splitting  the  hub  of  the  driving  gear 
housing  and  clamping  the  tube  by  means  of  four  bolts,  the  bolts 
passing  slightly  beneath  the  surface  of  the  tube  so  as  to  lock 
it  against  endwise  motion  (C,  Fig.  148).  What  is  probably  the 


236 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


best  method  of  making  a  built-up  axle  consists  in  the  use  of 
tapered  and  flanged  swaged  axle  tubes  which  are  bolted  to  the 
driving  gear  housing,  as  shown  at  D,  Fig.  148. 

In  order  to  insure  a  rigid  axle  housing  it  is  necessary  to  have 
a  relatively  long  bearing  for  the  axle  tube  in  the  hub  of  the 
driving  gear  housing.  This  bearing  is  generally  made  from 
two  to  two  and  a  half  times  the  outside  diameter  of  the  tube. 
With  the  best  class  of  workmanship  a  somewhat  smaller  length 
of  bearing  is  permissible.  It  is  also  advantageous,  from  the 
standpoint  of  rigidity,  to  make  the  driving  gear  housing  of  con- 
siderable width  in  the  transverse  direction  of  the  vehicle,  so  the 
tubes  need  not  be  so  long.  In  some  constructions  the  entire 
portion  of  the  axle  housing  between  wheel  hubs  is  made  in  two 


FIG.  149.— FLANGED  OUTER  END  OF  AXLE  TUBE  RIVETED  TO 
COMBINED  BRAKE  SUPPORT  AND  BEARING  HOUSING. 

castings,  and  short  tubes  are  inserted  into  these  for  the  wheels 
to  run  upon.  Constructions  may  be  found  ranging  all  the  way 
from  this  extreme  to  that  in  which  the  tubes  extend  close  up  to 
the  differential  bearings. 

In  a  plain  live  or  semi-floating  axle  a  bearing  housing  has  to 
be  provided  at  the  outer  end  of  the  axle  tube.  While  it  is  pos- 
sible to  expand  the  tube  itself  for  this  purpose,  this  construction 
is  rarely  seen.  The  bearing  housing  is  usually  made  in  a  separate 
piece  which  is  forced  into  or  over  the  end  of  the  axle  tube  and 
secured  by  riveting  or  brazing.  In  one  construction,  illustrated 
in  Fig.  149,  the  axle  tube  is  flanged  at  the  outer  end  and  riveted 
to  a  casting  which  forms  the  brake  carrier  and  bearing  housing. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


237 


Stresses  on  Axle  Tubes — In  discussing  the  stresses  on  the 
housing  of  a  driving  axle  we  have  to  consider  three  distinct 
cases,  viz. : 

(1)  When  the  car  is  being  started; 

(2)  When  the  car  is  being  driven; 

(3)  When  the  car  is  being  braked. 

The  first  two  cases  are  similar  in  that  the  kinds  of  stresses 
produced  are  the  same,  only,  since  the  clutch  will  transmit  a 


FIG.  ISO.— LOADS  ON  HOUSING  CORRESPONDING  TO  FORWARD 
DRIVING. 

greater  torque  than  the  motor  is  capable  of  developing,  if  the 
former  should  be  allowed  to  grip  suddenly,  the  flywheel  inertia 
would  cause  a  greater  torque  to  be  impressed  on  the  rear  axle 
than  would  ever  occur  in  regular  driving.  Just  how  much 
greater  it  would  be  it  is  impossible  to  determine.  When  the  car 


238  iSEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

is  being  started  or  driven  forward  the  loads  and  reactions  on 
the  axle  structure  are  as  shown  in  Fig.  150.  There  is  a  down- 
ward pressure  w  on  each  of  the  two  spring  saddles.  Then  there 
is  the  weight  uh  of  the  axle  itself,  which  may  be  considered  con- 
centrated at  the  centre.  Then  there  are  also  the  loads  b  b  on 
the  differential  bearings,  the  load  b'  on  the  pinion  bearing  and 
the  reaction  c  at  the  point  of  support  of  the  torque  arm  on  the 
frame.  Finally  there  is  the  reaction  P  of  the  road  surface  on  the 
driving  wheel  causing  the  forward  motion  of  the  car. 

It  can  easily  be  shown  that  the  bearing  loads  b  b  are  equal  to 
b',  hence  the  pressures  on  the  inner  bearings  create  no  stress  in 
the  axle  tubes.  Also,  the  moments  of  forces  b'  and  c  around  the 
rear  axle  axis  are  equal  and  opposite,  and  therefore  have  no 
effect  on  the  axle  tubes.  There  remain  only  the  vertical  bending 
moments  due  to  the  weights  w  w  on  the  spring  seats,  the  vertical 
bending  moment  due  to  the  weight  wi  of  the  axle,  and  the  hori- 
zontal bending  moment  due  to  the  propelling  thrust  P. 

When  the  brakes  are  applied  we  have  the  same  moments  in 
the  vertical  plane  due  to  the  weight  resting  on  the  spring  seats 
and  the  weight  of  the  axle.  The  horizontal  moment  is  in  the 
opposite  direction  and  is  proportional  to  the  maximum  braking 
force  instead  of  to  the  maximum  propelling  force,  which  former 
is  at  least  equal  to  the  latter.  In  addition  we  have  in  this  case 
a  torsion  moment  on  the  tubes,  since  the  brake  supports  are  se- 
cured to  the  outer  ends  of  the  axle  tubes,  and  when  the  brakes  are 
applied  the  friction  between  brake  band  and  drum  tends  to  carry 
the  brake  supports  around  with  the  drums.  This  tendency  is 
counteracted  by  the  torque  tube  or  rod  which  is  generally  fixed 
to  the  axle  housing  near  its  middle. 

It  will  thus  be  seen  that  when  braking,  the  axle  tubes  are  sub- 
jected to  the  same  bending  stresses  as  when  driving,  and,  besides, 
they  are  subjected  to  torsion.  Hence  the  combined  stress  is 
greatest  when  the  brakes  are  applied,  and  only  this  case  needs 
to  be  considered.  Owing  to  the  fact  that  the  weight  of  the  axle 
is  not  known  in  advance,  and  since  it  is  small  in  comparison 
with  the  weight  on  the  springs,  it  is  advisable  to  neglect  this 
factor. 

In  respect  to  the  vertical  load,  the  axle  housing  forms  a  beam 
freely  supported  at  both  ends  and  loaded  at  the  centre  and  two 
intermediate  points,  the  equivalent  point  of  support  being  at  the 
centre  of  the  road  wheel  in  the  case  of  a  full  floating  axle  and  at 
the  centre  of  the  outboard  bearing  in  the  cases  of  semi-floating 
and  plain  live  axles.  The  bending  moment  increases  from  noth- 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  239 

ing  at  the  point  of  support  to  the  maximum  at  the  centre  of  the 
spring  seats  and  is  constant  between  spring  seats.  (See  Fig.  151.) 

In  respect  to  the  horizontal  bending  moment,  each  half  of  the 
axle  may  be  considered  as  a  cantilever,  the  middle  of  the  axle 
being  the  fixed  end  of  the  lever  and  the  load  being  applied  to 
the  outer,  free  end.  The  variation  of  all  of  the  moments  is  shown 
in  the  three-plane  diagram,  Fig.  151. 

Now,  let  us  take  any  section  of  the  tube  inside  the  spring  seat 
at  a  distance  x  from  the  centre  plane  of  the  road  wheel.  The 


FIG.  151. — BENDING  MOMENTS  ON  AXLE  TUBE. 

A,  Bending  Moment  Due  to  Weight  on  Springs;  B,  Bending  Moment 
Due  to  Axle  Weight;  C,  Bending  Moment  Due  to  Retarding  Force  of  Rear 
wheels. 

moment  at  this  section  due  to  the  weight  on  the  spring  seat 
is  wl,  and  the  moment  due  to  the  retarding  force  of  the  brakes 
is  P  x.  The  maximum  retarding  force  P  is  reached  when  the 
wheels  are  locked  on  dry  macadam  surface,  under  which  condi- 
tion the  coefficient  of  friction  with  rubber  tired  wheels  is  about 
0.6.  Hence,  P  =  o.6  w  and  P  x  =  o.6  w  x.  These  two  bending 
moments  are  in  planes  at  right  angles  to  each  other  and  their 


240  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

resultant  (Fig.  152)   is  equal  to  the  square  root  of  the  sum  of 
their  squares.     That  is, 


Denoting  the  radius  of  the  road  wheel  by  r,  the  torsional  mo- 
ment on  the  axle  tube  is 

Aft  =  Pr  =  0.6  w  r. 
The  unit  bending  stress  is 

_  M*c 

*J  b  "*~     j 

/ 

and  the  unit  torsional  stress,  , 

Mtc 

St  =  -  . 
/     . 
The  combined  stress  is 


21       \\  j 

Remembering  that  for  a  circle  /  =  21,  we  may  write  this  in 
the  form 


Now  let  D  denote  the  outside  diameter  of  the  axle  tube  and 
d  the  inside  diameter.    Then 

D 

and  2~ 


64 

Inserting  these  values  and  those  of  ,Mt  and  Mb  found  above,  in 
equation  (46)  we  get 

D 

2 


_  ^ 

•S'c=0     ._,     -w      /2  +  0.36  x*  +  w  "VO^r2  +  P  +  0.36 

£T(U  —  d 

64 

SDw 


+  0.36  S  +      f  +  0.36  xz  +  0.36  r2 


&—P 

Denoting  the  part  in  parentheses  by  3;  we  may  write 

D*  Sc  —  5  D  w  y  =  d  *  S° 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


241 


d  ^==~- 
and  replacing  the  value  of  y — 


'(48) 


St 

The  great  majority  of  rear  axles  are  provided  with  trusses. 
No  matter  how  strongly  a  rear  axle  housing  is  constructed,  un- 
less it  is  provided  with  an  under  running  truss  it  will  sag  slightly 
in  the  middle.  This  causes  the  rear  wheels  to  spread  at  the 
bottom,  which  makes  for  an  unsightly  appearance  and  poor  work- 
ing conditions  of  the  bearings.  By  means  of  the  under  running 
truss  the  axle  tubes  can  be  practically  entirely  relieved  of  vertical 
bending  stresses.  In  that  case 'only  two  stresses  are  to  be  con- 
sidered, viz.,  the  torsional  stress  and  the  horizontal  bending  stress. 


FIG.  152.  —  COMPOSITION  OF  BENDING  MOMENTS  AND  COUPLE 
ON  AXLE  TUBE. 

The  value  of  the  latter  is  0.6  w  x.     Substituting  the  values  for 
this  case  in  equation  (46)  we  have 


By  the  same  processes  as  used  in  the  preceding  case  we  then 
find  that 


'=y  Z?*- 


3  D  zv (x  -f 


(50) 


242  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

The  stress  5"c  may  be  chosen  at  15,000  Ibs.  per  square  inch  for 
carbon  steel  tubing,  and  20,000  Ibs.  per  square  inch  for 
nickel  steel  tubing.  In  determining  the  diameters  of  the  tube,  the 
outside  diameter  is  usually  chosen  about  twice  the  diameter  of 
the  axle  shaft,  and  the  required  inside  diameter  may  then  be 
calculated  by  equation  (48)  or  (50).  Steel  tubing  has  been 
standardized  by  the  Society  of  Automobile  Engineers  and  the 
standard  sizes  should  be  selected.  (See  Appendix.) 

To  illustrate  the  use  of  the  equations  we  will  calculate  the 
necessary  diameters  of  axle  tubes  for  a  car  carrying  2,000  pounds 
on  the  rear  axle,  having  wheels  32  inches  in  diameter  and  in 
which  the  distance  x  from  the  centre  plane  of  the  rear  wheel  to 
the  point  where  the  axle  tube  enters  the  hub  of  the  driving  gear 
housing  is  18  inches.  The  weight  on  the  rear  axle  corresponds 
to  that  in  the  average  five  passenger  touring  car,  loaded,  and  we 
may  assume  that  it  is  medium-powered  and  has  rear  axle  driving 
shafts  i%  inches  in  diameter.  Hence  the  outside  diameter  of 
the  axle  tubes  might  be  made  2l/2  inches.  We  then  have 

D  =  2l/2  inches, 

r  =  16  inches, 

*  =  18  inches, 

w=i,ooo  Ibs. 

Assuming   that   the   tubes   are   to   be   of   carbon   steel,   we   put 
S0  =  15,000.     Inserting  values  in  equation  (50)  we  have 


-  /  =  z.  06  inches 
15,000 

This  is  the  minimum  section  for  any  point  between  the  brake 
support  and  the  driving  gear  housing.  Beyond  the  brake  sup- 
port the  axle  tube  is  subjected  to  bending  stresses  only.  Since 
the  truss  rod  is  generally  anchored  to  the  brake  support,  the 
vertical  bending  moment  comes  on  this  part  of  the  tube  whether 
the  axle  is  provided  with  a  truss  rod  or  not.  The  inside  diameter 
of  the  tube  at  this  point  would  generally  be  made  about  l/%  inch 
larger  than  the  diameter  of  the  axle  shaft  and  the  outside  diameter 
calculated  to  give  a  unit  stress  of  15,000  or  20,000  pounds  per 
square  inch  under  the  combined  bending  moments.  The  outside 
diameter  of  the  tube  would  then  be  made  such  as  to  correspond 
with  the  bore  of  the  next  largest  size  of  bearing.  However,  if 
the  axle  tube  is  continued  through  the  wheel  hub  with  the  same 
thickness  of  wall  as  it  has  between  the  spring  seat  and  the  driving 
gear  housing,  the  outer  portion  of  the  tube  will  be  amply  strong. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


243 


Pressed  Steel  Housing — Pressed  steel  presents  the  same 
advantages  for  rear  axles  as  it  does  for  other  parts  subjected  to 
varying  loads  and  to  shock.  It  gives  the  maximum  strength  for 


FIG.  153.— FIAT  PRESSED  STEEL  AXLE. 

a  given  weight,  and  when  a  sufficient  number  of  parts  are  needed 
to  make  the  pro  rata  cost  of  the  dies  small,  pressed  steel  parts 
are  usually  lower  in  cost  than  equivalent  parts  made  by  other 
processes. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE  24b 

One  of  the  earliest  automobile  concerns  to  bring  out  a  pressed 
steel  rear  axle  was  the  Fiat  Automobile  Company,  of  Turin,  Italy, 
whose  axle  is  illustrated  in  Fig.  153.  In  this  design  the  entire 
rear  axle  and  propeller  shaft  housing  are  made  in  two  identical 
pressed  steel  parts  which  are  bolted  together.  The  housing  is 
heavily  ribbed  and  is  used  without  a  truss  rod.  A  large  drop 
forged  fork  surrounds  the  forward  end  of  the  propeller  shaft 
housing  and  is  hinged  to  a  cross  member  of  the  frame.  The 
differential  and  driving  shaft  bearings  are  carried  by  a  frame 
riveted  into  the  enlarged  portion  at  the  middle  of  the  pressed 
steel  housing. 

Another  type  of  pressed  steel  axle  is  represented  by  the  Timken 
shown  in  Fig.  154.  In  this  case  the  housing  has  two  large  open- 
ings, in  the  front  and  rear  respectively.  It  is  pressed  from  sheet 
steel,  in  halves  which  are  welded  together  by  the  oxy-acetylene 
process.  In  the  axle  illustrated  the  joint  is  in  the  horizontal 
plane,  while  in  another  it  is  in  the  vertical  plane  and  the  welded 
joint  forms  a  strengthening  rib. 

A  third  type  of  pressed  steel  axle  which  is  used  on  several 
makes  of  American  low  priced  cars  made  in  very  large  numbers 
is  illustrated  in  Fig.  155.  The  axle  housing  is  made  in  halves 
which  are  joined  in  a  vertical  plane  at  the  centre  of  the  driving 
gear.  Each  half  is  again  made  of  two  parts,  viz.,  the  central 
casing  which  is  made  by  the  swaging  process,  and  a  plain  tube 
which  is  joined  to  the  latter  by  the  oxy-acetylene  welding  process. 

For  cars  of  small  size  and  in  which  the  springs  are  sup- 
ported on  the  axle  close  to  the  road  wheels,  so  that  the  bending 
moment  is  small,  pressed  steel  axle  housings  can  be  made  of 
y8  inch  stock.  For  touring  cars  of  moderate  size  the  axle 
housings  are  made  of  3/16  inch  stock,  the  diameter  of  the 
housing'  increasing  with  the  weight  of  the  car  from  2%  inch 
for  a  2,000  Ibs.  car  to  3  inch  for  4,000  Ibs.  car.  The  material 
used  in  these  housings  is  a  low  carbon  steel  having  an  elastic 
limit  of  about  34,000  Ibs.  per  square  inch.  In  a  full  floating 
axle  the  maximum  stress  comes  at  the  point  where  the  spring 
seats  are  attached,  and  in  order  to  avoid  the  necessity  of  using 
comparatively  heavy  material  for  the  whole  housing,  alloy 
steel  reinforcing  tubes  are  forced  into  the  housing  at  this 
point  and  are  supported  near  the  centre  of  the  axle. 

Gear  Carrier — With  the  type  shown  in  Fig.  154  it  is  com- 
mon to  carry  all  of  the  bearings  for  the  differential  gear  and 
driving  pinion  on  a  structure  known  as  the  gear  carrier  or  dif- 
ferential carrier,  which  is  bolted  to  the  pressed  steel  housing.  In 
some  designs  this  carrier  forms  the  closure  for  the  front  opening" 


246          BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

A 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


247 


in  the  pressed  steel  housing  and  has  the  torque  tube  or  rod  secured 
to  it,  while  in  other  cases  it  is  inserted  through  the  rear  opening 
and  bolted  to  the  rear  flange  of  the  housing,  but  does  not  serve 
as  a  cover  for  this  opening.  The  use  of  a  differential  carrier  has> 
the  advantage  that  all  of  the  bearings  for  the  driving  gear  are 
carried  in  a  single  integral  part  and  cannot  be  thrown  out  of 
alignment  by  the  stresses  on  the  axle  housing.  Moreover,  the 
bearings  can  be  adjusted  before  the  axle  is  assembled. 

Drop  Forged  Axles — Drop  forged  axles  present  substantially 
the  same  advantages  as  pressed  steel  axles.  They  do  not  require 
any  welding  to  be  done  upon  them,  and,  besides,  they  permit  of 
variations  in  the  thickness  of  the  walls  at  different  points  and  of 
integral  flanges  for  the  spring  seats,  etc.  The  advantage  over  the 


FIG.  157.— DIAGRAM  OF  ARCHED  AXLE  AND  DISHED  WHEELS. 

pressed  steel  axle  that  no  welding  is  required  is  offset,  however, 
by  the  fact  that  the  tubular  portions  must  be  bored  out.  One 
design  of  drop  forged  housing  is  shown  in  Fig.  156.  The  central 
portion  of  this  particular  housing  is  in  the  form  of  a  ring,  and  a 
gear  carrier  and  a  large  rear  cover  plate  are  used.  Ten  bolts 
pass  through  the  flange  of  the  gear  carrier  and  that  of  the  cover 
plate,  but  only  four  of  these  pass  through  holes  in  the  drop 
forged  housing.  The  housing  is  heavily  ribbed  between  the 
annular  and  tubular  portions  and  no  truss  rod  is  used. 

Arched  Rear  Axles— Dished  wood  wheels  present  considerable 
advantage  over  plain  wheels  in  the  way  of  strength,  and  on  horse 
vehicles  these  wheels  are  used  exclusively.  But  in  order  to  run 
properly,  dished  wheels  must  be  mounted  on  a  cambered  axle 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

whose  "set"  is  equal  to  the  angle  of  dish  of  the  wheel,  so  that  the 
lowermost  spoke,  which  carries  the  load  on  the  wheel,  stands  in 
a  vertical  position.  (See  Fig.  157.)  It  is  customary  to  give  a 
slight  "set"  to  the  front  wheel  spindles,  and  when  the  side  chain 
drive  was  common  the  rear  axle  spindles  also  were  often  given  a 
set  of  a  few  degrees,  the  flexibility  of  the  chain  making  this 
possible.  With  the  ordinary  design  of  shaft  driven  rear  axle, 
however,  it  is  impossible  to  incline  the  rear  axle  spindles,  and  if 
it  is  desired  to  employ  dished  road  wheels  it  is  necessary  to  re- 


FIG.  158.— CENTRAL  PORTION  OF  PEERLESS  ARCHED  AXLE. 


sort  to  special  constructions.  One  plan  consists  in  dividing  each 
rear  axle  shaft  into  two  parts  and  connecting  these  parts  by 
some  form  of  universal  joint  This  construction  is  exemplified 
in  the  Peerless  rear  axle  shown  in  Fig.  158.  The  axle  tubes  are 
set  into  the  driving  gear  housing  at  an  angle  equal  to  the  desired 
angle  of  set,  and  an  internal  and  spur  gear  type  of  universal  joint 
is  used. 

In  another  design  the  differential  gear  is  mounted  upon  an 
extension  of  the  propeller  shaft,  as  shown  in  Fig.  159.  Each 
master  gear  is  provided  with  a  long  sleeve  which  carries  a  bevr* 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

pinion  at  its  outer  end.  The  two  pinions  mesh,  respectively,  with 
bevel  gears  secured  to  the  rear  axle  driving  shaft  In  order  that 
there  may  be  no  interference  between  the  two  sets  of  bevel  gears, 
the  two  pinions  are  made  of  different  pitch  diameters,  and  the 
two  gears  the  same,  but  of  course  the  ratio  between  the  number 
of  teeth  in  the  pinion  and  gear  is  the  same  for  both  sets.  This 
construction  has  the  advantage  that  the  differential  gear  is  driven 
at  a  relatively  high  rate  of  speed  and  therefore  can  be  made 
smaller.  The  differential  is  operated  in  a  somewhat  unusual  man- 
ner in  that  power  is  applied  to  the  pinion  spider  through  the 


FIG.  159.— ARCHED  AXLE  WITH  DIFFERENTIAL  ON  PROPELLER 
SHAFT. 

central  shaft  instead  of  through  the  differential  housing  or  frame, 
as  ordinarily.  This  type  of  rear  axle  is  used  by  the  Daimler 
Motor  Company  in  Germany  and  by  the  La  Buire  Automobile 
Company  in  France.  It  is,  of  course,  obvious  that  with  this  con- 
struction the  axle  tubes  may  be  inclined  at  any  angle  desired. 

Types  of  Bearings — Anti-friction  bearings  are  used  almost 
exclusively  on  live  rear  axles,  and  all  of  the  different  types  are 
well  represented  in  this  part  of  the  car.  In  addition  to  the  radial 
load  resulting  from  the  weight  of  the  frame  and  body  carried 
on  the  axle,  and  from  the  reaction  of  the  bevel  gears,  there  arp 


250  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

thrust  loads  due  to  driving  on  one  side  of  a  strongly  crowned 
road  or  to  skidding  and  to  the  reaction  of  the  bevel  gears.  AH 
these  thrust  loads  must  be  provided  for  in  some  way.  Owing  to 
the  fact  that  the  thrust  load  in  skidding  may  assume  very 
considerable  values  and  that  radial  ball  bearings  should  not  be 
subjected  to  thrust  loads  of  more  than  10  per  cent  of  their 
radial  load  capacity,  a  great  many  rear  axles  are  fitted  with  some 
form  of  combined  radial  and  thrust  bearing.  When  bearings  are 
used  which  do  not  take  any  thrust  load  whatever,  as,  for  in- 
stance, cylindrical  roller  bearings,  it  is  absolutely  necessary  to 
provide  special  thrust  bearings.  It  is  not  customary  to  provide 
thrust  bearings  inside  the  rear  wheel  hubs  when  radial  ball  bear- 
ings are  fitted.  These  bearings  are  generally  of  considerable  size, 
and  are  depended  upon  to  carry  the  thrust  load  as  well.  In  some 
designs  of  axles  the  thrust  load  is  transmitted  from  the  wheels 
through  the  axle  shafts  to  the  thrust  bearings  at  the  side  of  the 
differential  gear.  In  the  latter  case  it  is  necessary  that  the 
axle  shaft  be  securely  fastened  to  the  master  gear  of  the  differen- 
tial as  well  as  to  the  road  wheel  hub. 

Bearing  Pressures — Taking  up  first  the  bearings  for  the 
bevel  pinion  shaft,  there  are  two  general  arrangements.  The 
most  common  of  these  consists  in  mounting  the  shaft  in  two 
bearings,  both  back  of  the  pinion,  one  as  close  to  it  as  possible 
and  the  other  a  considerable  distance  away.  The  other  method 
consists  in  placing  one  bearing  on  either  side  of  the  pinion.  The 
total  bearing  load  is  much  smaller  when  the  pinion  is  mounted 
between  bearings,  and  this  arrangement,  no  doubt,  would  be 
used  much  more  extensively  if  it  were  not  so  difficult  to  find 
sufficient  room  for  the  inner  bearing.  As  it  is,  some  bearing 
makers  rather  oppose  the  latter  arrangement  on  the  ground  that 
too  small  bearings  are  generally  used  on  the  inner  side  of  the 
pinion,  and  much  trouble  is  experienced  in  consequence.  Owing 
to  the  fact  that  the  spur  type  differential  gear  has  no  projecting 
hubs  on  its  circumference,  this  type  is  preferable  where  a  bearing 
is  to  be  placed  on  the  inner  side  of  the  pinion.  If  the  bevel  type 
of  differential  is  used  it  is  customary  to  place  it  on  the  back  side 
of  the  bevel  gear,  if  an  inner  bearing  is  to  be  fitted  on  the  pinion 
shaft. 

A  modification  of  the  first  design  described  is  that  in  which 
the  forward  end  of  the  propeller  shaft  tube  rides  on  the  propeller 
shaft  through  the  intermediary  of  a  ball  bearing.  In  this  case 
there  is  only  a  single  bearing  at  the  bevel  pinion,  and  the  load 
on  the  bearing  is  less  than  it  would  be  if  there  were  another 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


251 


bearing  close  to  it.    However,  while  the  bearing  load  is  reduced 
the  stress  in  the  propeller  shaft  is  increased. 

Besides  the  radial  load  the  pinion  shaft  is  subjected  to  thrust 
loads.  There  is,  first,  the  end  thrust,  due  to  the  tooth  reaction 
of  the  bevel  gears.  With  straight  bevel  gears  this  is  always  in 
the  forward  direction  and  is  comparatively  slight.  Besides 
this,  there  is  a  thrust  load  due  to  the  friction  at  the 
sliding  joint  in  the  propeller  shaft.  This  changes  in  direc- 
tion with  the  direction  of  slippage  at  the  joint  and  varies  in  value 
according  to  the  mean  radius  from  the  axis  of  rotation  of  the 


FIG;  160.— P INION  SHAFT 
MOUNTING  WITHOUT  THRUST 
BEARING. 


FIG.  161.— PINION  SHAFT 
MOUNTING  WITH  SINGLE 
THRUST  BEARING. 


surfaces  on  which  the  slippage  takes  place,  and  according  to  the 
state  of  their  lubrication.  This  load  is  greatest  when  a  squared 
or  fluted  shaft  type  of  slip  joint  is  employed,  and  smallest  with 
the  block  and  trunnion  type  of  joint.  When  the  sliding  takes 
place  in  one  direction  the  thrust  load  due  to  this  cause  adds  to  that 
due  to  the  tooth  reaction,  whereas  if  it  takes  place  in  the  opposite 
direction,  the  two  end  thrusts  are  opposed  and  the  resultant  may 
possibly  be  directed  backward. 

The  bevel  pinion  end  thrust  in  the  case  of  straight  bevel  gears 
varies  considerably  with  changes  in  the  gear  reduction  ratio. 
With  large  gear  reduction  ratios  and  block  and  trunnion  type 
slip  joints  it  is  quite  possible  to  take  up  the  end  thrust  on  the 
radial  ball  bearings,  which,  as  already  pointed  out,  have  a  thrust 


252  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

load  capacity  of  10  per  cent,  of  their  radial  load  capacity.  A 
design  in  which  end  thrust  in  both  directions  is  taken  up  on 
radial  bearings  is  shown  in  Fig.  160.  In  this  construction  it  is 
essential  that  the  measurements  x  and  y  be  exactly  alike,  as 
otherwise  the  bearings  will  be  cramped  when  the  inner  races  are 
drawn  tight  on  the  shaft.  Both  outer  races  are  close  up  against 
a  shoulder  at  one  end,  but  are  free  at  the  other  end. 

In  the  design  shown  in  Fig.  161,  end  thrust  in  the  forward  di- 
rection is  provided  for  by  a  special  ball  thrust  bearing.  This 
construction  is  suitable  where  the  bevel  gear  gives  a  small  re- 


FIG.  162. — PINION  SHAFT  MOUNTING  WITH  DOUBLE  THRUST 
BEARINGS. 

duction  and  the  slip  joint  is  of  the  block  and  trunnion  type,  so 
that  there  is  little  chance  of  the  end  thrust  ever  changing  in 
direction.  These  designs  can  be  used  with  straight  gears  only. 

The  most  highly  developed  design  provides  double  thrust  bear- 
ings on  the  pinion  shaft,  as  shown  in  Fig.  162.  In  this  design  a 
central  thrust  plate  is  clamped  between  collars,  which  in  turn 
are  clamped  between  a  shoulder  in  the  bearing  housing  and  the 
end  plate.  This  thrust  plate  forms  part  of  the  double  thrust 
bearing,  which  is  assembled  on  a  sleeve  mounted  on  the  pinion 
shaft.  This  sleeve  also  serves  as  a  spacer  for  the  radial  ball 
bearings,  the  inner  races  of  both  of  which  are  securely  clamped  to 
the  shaft,  while  the  outer  races  are  free  to  move  endwise.  With 
this  construction  the  pinion  is  held  positively  endwise,  thus  insur- 
ing continued  accuracy  of  mesh,  and  the  radial  bearings  are  re- 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE 


253 


lieved  of  all  thrust  loads,  and  consequently  operate  at  their  high- 
est efficiency. 

It  will  be  seen  that  the  construction  Fig.  162,  which  takes 
account  of  all  possible  bearing  loads,  is  somewhat  complicated 
and  for  this  reason  many  designers  prefer  combined  radial  and 
thrust  bearings  for  the  pinion  shaft,  such  as  conical  roller  bear- 
ings, cup  and  cone  ball  bearings,  etc.  Fig.  163  illustrates  a  pinion 
shaft  mounted  in  two  conical  roller  bearings.  The  outer  rings 
of  the  roller  bearings  lie  close  up  to  internal  flanges  on  the 


FIG.  163.— PINION  SHAFT  MOUNTED  IN  CONICAL  ROLLER  BEARINGS. 

bearing  housing  at  their  inner  ends,  and  both  of  the  bearings 
can  be  adjusted  by  means  of  a  single  nut  and  check  nut  at  the 
outer  end,  which  are  very  accessible.  This  design  also  provides 
means  for  adjusting  the  mesh  of  the  gears,  consisting  of  an  inner 
and  an  outer  housing,  the  inner  housing  being  screwed  into  the 
outer  one  and  locked  in  position  when  the  gears  have  once  been 
properly  adjusted.  This  type  of  bearing  is  very  popular  in  con- 
nection with  helical  bevel  gear  drives. 

The  Hyatt  type  of  flexible  roller  bearing  is  also  used  to  some 
extent  on  pinion  shafts.  A  typical  mounting  of  these  bearings  is 
shown  in  Fig.  164.  The  outer  sleeve  of  the  bearing  is  pressed 
into  the  bearing  housing  and  held  from  rotating  by  means  of  a 


254 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


set  screw.  The  inner  sleeve  is  forced  over  the  pinion  shaft,  and 
its  forward  end  presses  against  a  thrust  plate,  forming  one 
member  of  a  ball  thrust  bearing,  the  other  plate  of  which  bears 
against  an  adjusting  nut  screwed  into  the  bearing  housing.  This 
design  is  intended  for  cars  with  only  a  single  universal  joint  in 
the  propeller  shaft,  and  the  forward  end  of  the  shaft  is  to  be  car- 
ried in  another  roller  bearing,  designated  a  "steadying  bearing." 
Calculation  of  Pinion  Shaft  Bearings— In  determining  the 
proper  sizes  of  bearings  for  the  pinion  shaft  we  first  calculate 
the  torque  on  the  shaft  corresponding  to  full  engine  power  and 
direct  drive,  then  calculate  the  tooth  pressure  on  the  pinion,  based 
upon  the  mean  pitch  diameter  of  the  latter,  resolve  this  tooth 


FIG.  164.— PINION  SHAFT  MOUNTED  IN  HYATT  ROLLER  BEARINGS. 

pressure  into  a  radial  and  a  thrust  load,  and  finally  divide  the 
radial  load  between  the  two  bearings  supporting  the  pinion  shaft. 
The  method  of  calculation  may  be  illustrated  by  means  of  a 
practical  example  of  a  straight  bevel  gear  drive. 

We  will  take  the  case  of  an  engine  developing  a  maximum 
normal  speed  torque  of  ±08  pounds-feet  (four  cylinder,  4x5  inch). 
Suppose  that  the  bevel  pinion  has  16  teeth  of  five  pitch  and  the 
gear  54  teeth,  thus  givkig  a  reduction  of  3.5  to  I.  According  to 
equation  (44)  the  proper  width  of  face  for  the  pinion  would  be 

KA^    *33 — —  =  i . 205  —  say  i J  inches. 
54X3-2X0.63 

The  largest  pitch  diameter  of  the  gear  is  10.8  inches,  and  that  of 
the  pinion  3.2  inches.  Hence  the  distance  from  the  point  of  inter- 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  255 

section  of  the  two  largest  pitch  diameters  to  the  point  of  intersec- 
tion of  the  axes  of  the  pinion  and  gear,  respectively,  is 


>5  .  42  +  i  •  68  =  5  .  63  inches. 
The  middle  of  the  length  of  the  tooth  is  at  a  distance 

5.63  —  0.625  =  5  inches 

from  the  point  of  intersection  of  the  shaft  axes,  hence  the  mean 
pitch  diameter  of  the  pinion  is 

3  .  2  X  —  -  —  =  2.84  inches 

5-63 

and  the  mean  pitch  radius  is  1.42  inches.    The  tangential  pressure 
on  the  bevel  pinion  then  is 

108  *I2  =  gI2  pounds. 

1.42 

The  radial  component  of  this  pressure  can  be  found  by  means 
of  equation  (27)  after  the  angle  of  the  bevel  pinion  pitch  line 
with  the  axis  of  the  pinion  has  been  found.  The  tangent  of  this 
angle  is 

14=0.30 

10.8 

and  the  angle  is  found  to  be  equal  to  16°  42'.    Inserting  values  in 
equation  (27), 

Pr  =  -s/9122  -f  (912  X  o.  364  X  0.958)2  =  970  pounds. 
If  both  bearings  are  back  of  the  pinion,  as  in  Fig.  148,  the  dis- 
tance a  will  be  about  i*/&  inches  and  the  distance  b  5M$  inches. 
Hence  the  load  on  the  bearing  close  to  the  pinion  is 

970  X  —   =1,243  -pounds, 

4 
and  the  load  on  the  bearing  farthest  from  the  pinion, 

1,243  —  970  =  273  pounds. 

These  are  the  maximum  loads  on  the  bearings  when  the  car 
is  being  driven  through  the  direct  drive.     When  it  is  driven  on 
any  of  the  other  gears  the  maximum  loads  on  the  bearings  will 
be  equal  to  the  product  of  the  above  loads  by  the  reduction  ratio 
of  the  particular  gear.     For  instance,  if  the  low  gear  reduction 
ratio  of  the  change  gear  be  3.2,  then  the  maximum  load  on  the 
bearing  directly  back  of  the  pinion  would  be 
3.2x1,243  =  3,977  pounds 
and  that  on  the  other  bearing 


In  selecting  the  size  of  bearing  it  must  be  borne  in  mind  that 
the  rated  capacity  of  the  bearing  is  very  conservative,  and  that, 
on  the  other  hand,  it  is  a  very  rare  occurrence  that  the  motor 


256  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

operates  under  full  power  on  the  low  gear.  In  view  of  this  fact 
the  bearing  can  be  so  chosen  that  the  maximum  load  under  low 
gear  is  about  100  per  cent,  above  the  rated  capacity  of  the  bear- 
ing, or  that  the  rated  capacity  is  about  50  per  cent,  higher  than 
the  maximum  load  on  the  bearing  on  the  direct  drive.  For  the 
most  highly  loaded  bearings  the  heavy  series  of  ball  bearings  is 
usually  selected.  In  the  present  case  the  No.  407  would  probably 
be  chosen,  which  has  a  rated  capacity  of  1,900  pounds.  The  for- 
ward bearing  is  comparatively  lightly  loaded,  but  it  must  have 
a  bore  somewhat  larger  than  the  required  propeller  shaft  di- 
ameter. For  this  place  a  bearing  of  the  medium  series  would  be 
the  most  advantageous,  and  the  No.  307,  which  has  a  rated  load 
capacity  of  1,100  pounds,  would  probably  be  chosen. 

Now,  consider  the  case  where  the  bearings  are  placed  on  oppo- 
site sides  of  the  pinion,  as  in  Fig.  161.  The  distance  a  here 
measures  about  IT^  inches,  and  the  distance  b  i&  inches.  Hence 
the  load  on  the  inner  bearing  would  be 

r  3  ^T  5   X  97o  =  &i Pounds 

XT*  T  JT8 

and  that  on  the  outer  bearing 

970  —  461  =  509  pounds. 

It  will  be  seen  that  in  this  case  the  bearing  loads  are  much 
smaller  than  in  the  preceding  case.  The  space  available  for  the 
inside  bearing  is  rather  limited,  yet  a  somewhat  higher  factor  of 
safety  is  attainable  in  this  case  than  in  the  previous  one.  A  No. 
404  bearing,  having  a  rated  capacity  of  1,050  pounds,  could  be 
used  on  the  inner  end  of  the  pinion,  and  a  No.  307,  having  a 
rated  capacity  of  1,100  pounds,  on  the  other  end.  The  rated 
capacities,  therefore,  are  about  100  per  cent,  higher  than  the  maxi- 
mum bearing  loads  on  the  direct  drive.  If  the  outside  diameter 
of  the  bearing  is  limited  and  the  load  to  be  carried  is  large,  bear- 
ings of  the  so-called  heavy  series  should  always  be  selected.  In 
Fig.  161,  in  order  to  throw  as  much  of  the  bearing  load  as  pos- 
sible on  the  bearing  back  of  the  pinion,  the  pinion  is  provided 
with  a  projecting  hub,  and  the  bearing  on  -the  inside  is  located  at 
some  distance  from  the  pinion  proper.  This,  of  course,  can  only 
be  done  where  the  differential  gear  is  entirely  back  of  the  bevel 
gear.  The  housing  for  the  inside  bearing  in  this  design  is  made 
cup-shaped,  so  as  to  permit  of  the  largest  possible  size  of  bear- 
ing without  sacrificing  strength  in  the  supporting  housing. 

Differential  Bearings — It  is  not  necessary  to  consider  the 
plain  live  axle  mathematically,  as  that  type  is  practically  obsolete 
In  nearly  all  modern  axles  the  inner  axle  bearings  are  mounted 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  257 

on  the  hubs  of  the  differential  housing,  and  with  the  full  floating 
type  of  axle  at  least  the  loads  on  these  differential  bearings  are 
due  solely  to  the  bevel  tooth  reaction.  The  normal  pressure  on 
the  teeth  of  the  gear  is  the  same  as  the  normal  pressure  on  the 
teeth  of  the  pinion,  and  the  tangential  pressures  on  gear  and 
pinion  are  also  the  same.  Hence — continuing  our  example — the 
tangential  force  on  the  gear  is  912  pounds.  The  pitch  line  angle 
of  the  gear  is  such  that  its  tangent  is 

10.8 

=  3.38 

3.2 

and  the  angle  is  found  to  be  equal  to  70°  30'.  Inserting  values  in 
equation  (27)  for  this  case  we  have 

P*  = -\J9122  +   (912  X  0.364  X  0.284)2  =  917  pounds. 
The  thrust  load  is  found  by  inserting  values  in  equation  (26)  as 
follows :  912  x  0  364  x  0  959  =  31g  pounds 

The  radial  load  is  divided  between  the  two  differential  bearings 
in  the  inverse  proportion  of  their  distances  from  the  centre  plane 
of  the  bevel  gear.  Owing  to  the  fact  that  these  bearings  must 
have  a  relatively  large  bore  in  comparison  with  the  load  they 
have  to  carry,  bearings  of  the  medium  series  are  usually  chosen 
if  radial  ball  bearings  are  to  be  used.  The  most  heavily  loaded 
of  these  bearings  usually  has  a  rated  load  capacity  50  to  100 
per  cent,  greater  than  the  maximum  load  coming  on  it  when  the 
car  is  driven  on  the  direct  drive.  In  many  cases  the  bevel  gear 
is  much  closer  to  one  bearing  than  to  the  other,  and  the  load  on 
one  bearing  therefore  is  much  greater  than  that  on  the  other. 
However,  notwithstanding  this  fact,  bearings  of  the  same  size 
are  frequently  chosen,  for  the  sake  of  symmetry  and  minimum 
number  of  different  parts.  In  any  case,  the  bore  of  one  bearing 
could  hardly  be  made  smaller,  and  all  that  could  be  done  would 
be  to  choose  a  bearing  of  the  light  series. 

End  Adjustment — With  the  highest  class  of  workmanship 
it  is  unnecessary  to  provide  means  for  longitudinal  adjustment 
of  the  bearings.  However,  since  measurements  have  to  be  taken 
from  the  pitch  lines  of  the  gears,  which  involves  considerable 
difficulty,  some  provision  is  usually  made  to  allow  of  adjusting 
the  mesh  of  the  gears.  The  simplest  means  consists  in  placing 
a  washer  back  of  the  thrust  bearing  and  another  washer  on  the 
opposite  side  of  the  differential  housing,  between  the  end  of  its 
hub  and  a  shoulder  on  the  inside  of  the  driving  gear  housing,  and 
changing  the  thickness  of  these  washers  until  the  gears  mesh 
properly.  Quite  a  number  of  designers,  however,  provide  screw 


258 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


adjustment  of  the  bearings.  Such  a  means  of  adjustment  is  illus- 
trated in  Fig.  165.  The  radial  bearing  is  mounted  in  a  bushing 
which  is  carried  in  the  bearing  support  forming  part  of  the  driv- 
ing gear  housing.  One  end  of  this  bushing  is  made  somewhat 
larger  in  diameter  than  the  other  end, 
and  is  threaded  on  the  outside,  the 
threaded  portion  screwing  into  corre- 
sponding internal  threads  on  the  bear- 
ing support.  The  outer  end  of  the 
bearing  bushing  has  an  internal  flange 
against  which  the  outer  plate  of  the 
thrust  bearing  rests,  and  by  screwing 
the  bearing  bushing  farther  into  or 
out  of  the  support  the  thrust  bearing 
can  be  moved  back  and  forth  in  the 
direction  of  its  axis.  A  lock  nut  is 
provided  for  locking  the  bearing  bush- 
ing when  the  adjustment  has  been 
made.  It  may  be  pointed  out  that 
when  a  pair  of  bevel  gears  has  once 
been  properly  adjusted  there  should 

FIG.    165.-ScR^TAD-  ^crwbear0ofatShrteef°h  cannot  b^com 
JUSTMENT  OF  BEVEL  GEAR.  JJ^S^to  by^SmeT' 

The  problem  of  endwise  adjustment  is  very  readily  solved  with 
conical  roller  or  cup  and  cone  bearings.  As  shown  in  Fig.  166, 
all  that  is  necessary  is  to  lodge  the  outer  race  or  ring  of  the 
bearing  in  a  suitable  recess  in  the  driving  gear  housing  and 
mount  the  inner  race  or  ring  on  the  end  of  the  differential  gear 
housing  hub,  making  the  inner  portion  of  this  hub  of  somewhat 
larger  diameter  and  threading  it,  and  passing  a  nut  over  this 
threaded  portion.  This  is  done  at  both  ends  of  the  differential 
gear,  and  by  means  of  the  two  nuts  the  differential  can  be  moved 
in  either  direction  at  will.  The  nuts  may  be  split  and  provided 
with  a  clamp  screw,  or  they  may  be  provided  with  any  other 
suitable  locking  device. 

Wheel  Bearings — The  wheel  bearings  support  the  loads  car- 
ried by  the  wheels  and  also  take  the  load  due  to  the  propelling 
and  braking  efforts.  We  found  that  the  limiting  value  of  the 
braking  effort  is  0.6  times  the  weight  resting  on  the  wheel,  and 
the  limiting  value  of  the  driving  effort  the  same.  Since  driving 
and  braking  efforts  act  at  right  angles  to  the  weight,  the  resultant 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


259 


of  the  two  simultaneous  loads  is  equal  to  the  square  root  of 
the  sum  of  the  squares,  viz.: 


However,  this  is  an  entirely  different  load  from  that  on  the 
differential  bearings,  for  instance.  The  actual  load,  owing  to  the 
unevenness  of  the  road  surface,  changes  from  instant  to  instant, 
and  at  times  greatly  exceeds  the  so-called  "dead"  load.  The 
maximum  load  to  which  the  bearings  are  ever  subjected  depends 
upon  the  weight  carried,  the  size  of  the  wheels,  the  width  of 
the  tires  and  the  state  of  their  inflation,  the  flexibility  of  the 
springs,  the  nature  of  the  road  surface,  the  speed  of  the  car,  etc. 
The  only  factor  that  can  be  taken  account  of  in  selecting  the 
bearings  is  the  load  carried  by  each  wheel.  The  bearings  should 
have  a  rated  load  capacity  from  50  to  100  per  cent,  higher  than 
the  maximum  load  they  will  have  to  carry,  provided  the  rated 
capacity  represents  ability  to  carry  uniform  loads. 

In  the  case  of  semi-floating  and  three-quarter  floating  axles,  the 
entire  load  on  each  wheel  is  carried  on  a  single  bearing,  whereas 


FIG.  166. — ENDWISE  ADJUSTMENT  OF  DIFFERENTIAL  MOUNTED  IN 
ROLLER  BEARINGS. 


260 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


in  the  case  of  full  floating  axles  it  is  carried  on  two  bearings. 
When  two  bearings  are  used  the  ideal  arrangement  in  some  re- 
spects would  be  to  place  them  symmetrically  on  opposite  sides  of 
the  centre  plane  of  the  wheel,  in  which  case  both  would  carry 
an  equal  load,  and  both  could  be  made  of  the  same  size.  How- 
ever, since  the  brake  and  brake  support  must  be  very  close  to  the 
spokes  of  the  wheel,  the  inner  bearing  generally  has  to  be  placed 
rather  close  to  the  centre  plane  of  the  wheel.  In  fact,  in  many 
designs  the  arrangement  is  such  that  the  inner  bearing  supports 
nearly  the  whole  load,  and  the  outer  bearing  serves  only  as  a 
"steadying"  bearing. 


FIG.  167. — DRIVING  WHEEL  HUB  MOUNTED  ON  Two  RADIAL  BALL 
BEARINGS. 

The  driving  effort  is  always  parallel  to  the  planes  of  the  rear 
wheels,  and  any  thrust  load  on  the  rear  wheel  bearings,  is  the 
result  of  sideward  inclination  of  the  road  surface,  centrifugal 
force  or  impact  due  to  skidding.  For  this  reason  it  is  not  essen- 
tial to  provide  thrust  bearings  in  the  hubs,  even  when  radial  ball 
bearings  are  used. 

Mounting  of  Wheel  Bearings — When  two  radial  ball  bear- 
ings are  used  in  the  wheel  hubs  of  a  full  floating  axle,  the  inner 
races  of  both  are  securely  clamped  to  the  axle  tube,  a  projection 
of  the  brake  support  hub  or  a  collar  forced  over  the  axle  tube 
against  the  shoulder  thereof  serving  as  a  stop;  a  tubular  spacer 
is  inserted  between  the  two  inner  races,  and  a  nut  is  screwed 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  261 


FIG.  16Q. — DRIVING  WHEEL  HUB  ON  SINGLE  BALL  BEARING, 
(THREE-QUARTER  FLOATING.) 


FIG.  169. — DRIVING  WHEEL  HUB  ON  HYATT  ROLLER  BEARING. 
(THREE-QUARTER  FLOATING.) 


262 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  263 

over  the  end  of  the  tube,  as  shown  in  Fig.  167.  The  outer  race 
of  only  the  inner,  larger  bearing  is  clamped  tight  in  the  hub,  so 
this  bearing  will  take  the  end  thrust  in  both  directions. 

In  the  so-called  three-quarter  floating  type  of  axle  only  a 
single  bearing  is  used  inside  the  wheel  hub,  as  shown  in  Fig.  168. 
This  bearing  must  be  located  in  the  centre  plane  of  the  wheel,  and 
both  of  its  races  must  be  secured  against  endwise  motion,  so  it 
will  take  both  radial  and  thrust  loads.  The  driving  dog  in  this 
design  of  axle  is  either  welded  to  the  axle  shaft  or  else  rigidly 
secured  to  it,  and  is  also  firmly  secured  to  the  wheel  hub.  The 
single  hub  bearing  may  be  either  a  radial  ball  bearing,  a  combined 
radial  and  thrust  ball  bearing  (Two-in-One),  as  shown  in  Fig. 
168,  or  a  cylindrical  roller  bearing,  as  shown  in  Fig.  169.  The 
latter  bearing,  of  course,  does  not  take  any  end  thrust,  and  in 
this  design  provisions  are  made  for  transmitting  the  end  thrust 
through  the  axle  shafts  to  the  thrust  bearings  at  the  sides  of  the 
differential  housing. 

A  similar  arrangement  was  suggested  by  F.  G.  Barrett  in  his 
paper  on  Ball  Bearings,  read  before  the  Institution  of  Automo- 
bile Engineers.  Mr.  Barrett's  suggested  design  is  shown  in  Fig. 
170.  A  double  ball  thrust  bearing  is  mounted  to  .one  side  of  the 
differential  gear.  The  outer  races  of  the  two  radial  bearings  in 
the  wheel  hub  are  clamped  tight,  but  the  inner  races  are  made  a 
free  fit  on  the  axle  tube  so  these  bearings  will  not  take  any  end 
thrust.  The  end  thrust  is  transmitted  through  the  wheel  hub, 
the  axle  shaft,  the  master  gear  of  the  differential,  the  differential 
spider,  the  other  master  gear  and  the  differential  housing  to  the 
double  ball  thrust  bearing,  which  latter  is  firmly  supported  by 
the  axle  housing.  The  practice  of  using  two  ball  thrust  bearings 
at  the  differential  is  quite  prevalent  in  Europe,  but  usually  one 
thrust  bearing  is  placed  on  either  side  of  the  differential,  whereas 
Mr.  Barrett  places  both  on 'the  same  side. 

Lubrication — The  rear  axle  housing  is  generally  filled  with 
non-fluid  oil,  and  in  order  to  prevent  this  from  working  through 
the  bearings  into  the  axle  tubes,  packings  are  generally  provided 
at  the  inner  ends  of  the  tubes,  as  illustrated  in  Figs.  158  and  159. 
It  is  a  good  idea  to  provide  a  plugged  hole  for  replenishing  the 
grease,  in  the  cover  plate  or  near  the  top  of  the  casing,  so  as 
to  make  it  unnecessary  to  remove  the  entire  cover  plate  for  this 
purpose,  and  a  drain  plug  should  be  provided  at  the  lowest  point 
of  the  casing,  so  all  lubricant  and  dirt  may  be  conveniently 
washed  out  with  gasoline  or  kerosene.  In  Europe  the  cases  are 
often  provided  with  large  filling  spouts. 


264 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


Truss  Rod— Probably  more  than  90  per  cent,  of  all  live  axle 
designs  have  an  under-running  truss  to  relieve  the  axle  housing 
of  the  vertical  bending  moment.  The  middle  of  the  truss  is  gen- 
erally retained  between  projections  at  the  bottom  of  the  gear 
case,  and  the  ends  are  secured  to  fittings  fastened  to  the  axle 
housing  between  the  spring  supports  and  the  end,  these  anchor- 
ages being  generally  integral  with  the  brake  support.  The  truss 
may  be  tightened  by  means  of  nuts  on  both  ends  outside  the 
brake  support,  or  by  means  of  a  turnbuckle,  as  shown  in  Fig.  171, 
in  which  latter  case  the  ends  of  the  rod  are  hinged  to  the  axle 
tube.  The  threaded  ends  of  the  rods  should  preferably  be  upset 
so  the  thread  will  not  reduce  the  strength  of  the  rod. 

The  downward  bending  moment  due  to  the  weight  on  the 
springs  at  any  point  between  the  spring  seats  is  w  I,  where  w 
is  the  weight  on  one  spring  seat  and  /  the  distance  between  the 


FIG.  171.— REAR  AXLE  TRUSS. 

centre  plane  of  the  wheel  and  the  centre  of  the  spring  seat.  The 
truss  produces  an  upward  bending  moment  which  is  a  maximum 
at  the  middle  of  the  axle  and  decreases  uniformly  toward  the 
truss  anchorages.  Its  bending  moment  diagram  therefore  is  a 
triangle,  whereas  the  diagram  of  the  bending  moment  due  to  the 
load  on  the  springs  is  a  trapezoid.  Consequently,  the  two  bend- 
ing moments  cannot  entirely  neutralize  each  other,  except  at 
certain  points. 

Let  T  be  the  tension  in  the  truss  rod.  Then  the  vertical  com- 
ponent of  this  force,  which  presses  upward  on  the  driving  gear 
housing  is  T  sin  0,  and  the  bending  moment  at  the  middle  of  the 
axle  housing  due  to  this  upward  pressure  is  T  I'  sin  0,  where  /' 
is  the  horizontal  distance  from  the  centre  of  the  axle  to  the  truss 
anchorage.  Since  the  angle  0  is  in  every  case  small,  it  is 
permissible  to  substitute  for  sin  0 

h 


which  makes  the  upward  bending  moment  T h.    The  permis- 
sible tension  T  in  the  rod,  of  course,  is  proportional  to  the 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  265 

cross  sectional  area  of  the  rod  or  to  the  square  of  its  diame- 
ter d.  hence  the  moment  is  proportional  to  d*  h.  The  upward 
bending  moment  due  to  the  truss  should  be  proportional  to 
the  downward  bending  moment  wl  due  to  the  weight  on  the 
springs.  Hence  we  may  write 

d2  h  ^  «//. 
and 


d~y  tfLi 
The  data  at  hand  shows  that  in  average  modern  practice 

d=J~^ri (so 

V    7,000  h 

The  actual  tension  in  the  truss  rods,  of  course,  depends  upon 
how  tightly  they  are  drawn  up,  and  the  load  that  must  be 
carried  by  the  truss  in  any  particular  design  depends  upon 
the  rigidity  of  the  axle  housing  itself.  A  large  part  of  the 
load  on  the  truss  results  from  the  shocks  on  the  unsprung 
weight  at  the  middle  of  the  axle,  and  if  this  weight  is  unusu- 
ally great,  as  in  the  case  of  a  transmission  axle,  for  instance, 
the  truss  may  be  made  somewhat  heavier  than  given  by  the 
formula. 

Rear  Axle  Torsion  and  Thrust— The  reaction  between  the 
teeth  of  the  bevel  gear  and  pinion  causes  a  pressure  on  the 
bearing  of  the  bevel  pinion  shaft,  and  this  pressure  tends  to 
cause  the  axle  housing  to  rotate  around  the  axle.  As  in  all 
similar  cases,  action  and  reaction  are  equal  and  opposite, 
and  the  axle  housing  tends  to  turn  "backward"  with  the  same 
torque  as  is  impressed  upon  the  axle  shafts  in  the  "forward" 
direction.  Therefore,  it  is  obvious  that  the  torsional  effect 
on  the  axle  housing  may,  under  certain  conditions,  as  in  driv- 
ing on  the  low  gear  under  full  engine  power,  assume  very 
high  values,  and  means  must  be  provided  to  prevent  the  hous- 
ing from  yielding  to  this  torque.  In  a  considerable  number  of 
cars  the  body  springs  are  depended  upon  to  keep  the  axle 
housing  in  position  against  the  torsional  reaction.  In  cars 
fitted  with  a  single  universal  joint  in  the  propeller  shaft  the 
latter  is  often  surrounded  by  a  so-called  torque  tube,  whose 
forward  end  may  have  a  bearing  on  the  propeller  shaft  or 
be  suspended  from  a  cross  member  of  the  frame,  and  whose 
rear  end  is  rigidly  fitted  into  the  rear  axle  housing.  In  cars 
with  two  universal  joints  a  torque  arm  rigidly  secured  to  the 
rear  axle  housing  extends  forward  to  a  frame  cross  member 
to  which  it  is  linked  in  some  manner. 


266  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

Besides  the  torsional  effect,  there  is  also  a  forward  thrust 
on  the  axle  housing.  All  of  the  propelling  effort  is  produced 
by  the  reaction  of  the  driving  wheels  on  the  ground,  whereas 
a  good  deal  of  the  resistance  to  motion  is  made  up  of  the 
road  resistance  encountered  by  the  front  wheels  and  the  air 
resistance  on  the  body.  The  force  necessary  to  overcome 
these  latter  resistances  must  be  transmitted  from  the  rear 
axle  housing  to  the  body.  On  the  other  hand,  when  a  car 
is  to  be  stopped  quickly,  by  the  application  of  the  brakes, 
most  of  the  kinetic  energy  that  has  to  be  dissipated  is  stored 
up  in  the  parts  supported  by  the  vehicle  frame,  whereas  the 
braking  resistance  takes  effect  at  the  ground  contact  of  the 
rear  wheels.  Hence  there  is  a  strong  retarding  pull  exerted 
by  the  rear  axle  housing  on  the  vehicle  frame,  which  in  the 
absence  of  special  members  is  transmitted  by  the  body 
springs.  However,  some  designers  provide  special  thrust  rods 
between  the  axle  housing  and  the  frame,  these  generally  ex- 
tending underneath  the  side  frame  members,  being  hinged  to 
both  connected  parts  so  as  to  allow  of  free  spring  action. 

frT  addition  to  the  torsion  and  thrust  on  the  rear  axle 
housing,  due  to  the  transmission  of  power,  the  axle  is  sub- 
jected to  other  stresses,  which  are  the  result  of  impacts  be- 
tween the  driving  wheels  and  road  obstructions.  ,  For  in- 
stance, if  one  of  the  driving  wheels  strikes  an  obstruction 
rising  some  distance  above  the  road  surface,  the  shock  tends 
to  throw  the  axle  out  of  alignment  with  the  frame.  This 
is  provided  against  in  some  designs  by  diagonal  brace  rods 
running  from  the  forward  end  of  the  torque  tube  to  the 
outer  ends  of  the  axle  housing.  On  the  other  hand,  the  axle 
must  be  allowed  freedom  of  motion  in  a  vertical  plane  so  it 
may  follow  the  irregularities  of  the  road  surface  without 
straining  any  portion  of  the  running  gear. 

Torque  Tubes — The  maximum  bending  moment  on  the  torque 
tube  or  torque  rod  may  be  calculated  on  the  basis  of  the 
torque  necessary  to  slip  the  rear  wheels  on  a  road  surface  on 
which  rubber  tires  have  a  friction  coefficient  of  0.6.  For 
instance,  if  the  rear  axle  carries  a  maximum  load  of  2,000 
pounds  and  the  wheels  have  a  radius  of  16  inches,  then  the 
maximum  torque  is 

1 6  x  2,000  x  0.6  =  19,200  pounds-inches. 

Suppose  that  the  distance  from  the  axis  of  the  rear  axle  to 
the  point  of  support  of  the  torque  tube  is  40  inches,  then 
the  maximum  reaction  of  the  support  is 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  267 

19,200  = 

40 

The  bending  moment  at  any  point  along  the  tube  may  then 
be  found  by  multiplying  this  reaction  by  the  distance  of  the 
particular  point  considered  from  the  point  of  support.  The 
most  important  point  in  this  connection  is  generally  where 
the  tube  enters  the  cast  fitting.  We  will  assume  this  distance 
to  be  24  inches.  Then  the  bending  moment  at  this  point  is 

24  x  480  =  1  1,520  pounds-inches. 

Owing  to  the  fact  that  the  torque  figured  on  is  not  the  normal 
working  torque  but  the  very  maximum  that  can  be  trans- 
mitted, only  a  small  factor  of  safety  need  be  figured  on.  With 
the  ordinary  carbon  steel  tubing  a  stress  of  25,000  pounds 
per  square  inch  can  be  allowed. 

The  maximum  forward  or  backward  thrust  of  the  rear  axle 
is  equal  to  the  adhesion  of  the  wheels  to  the  ground,  viz.: 

0.6  x  2,000  =  1,200  pounds. 

This,  too,  is  more  than  is  ever  attained  in  normal  operation; 
for,  assuming  the  car  with  load  to  weigh  3,200  pounds,  the 
propelling  effort  up  a  20  per  cent,  grade  at  low  speed  on  fair 
roads  is  only  about  720  pounds,  and  not  even  all  of  this  has 
to  be  transmitted  to  the  frame.  About  the  only  condition 
under  which  a  thrust  of  1,200  pounds  would  be  attained  is 
when  the  wheels  are  locked  by  the  brakes. 

Owing  to  the  fact  that  the  bending  moment  varies  from 
nothing  at  the  point  of  support  to  the  maximum  at  the  joint 
of  the  tube  to  the  driving  gear  housing,  it  is  customary  to 
reinforce  the  rear  end  of  the  tube  by  slipping  another  tube 
over  it  or  into  it.  The  forward  end  of  the  reinforcement 
should  be  tapered  down  to  a  sharp  edge  so  as  to  avoid  an 
abrupt  change  in  section  tending  to  localize  the  stresses,  and 
in  the  case  of  an  outside  reinforcement  also  for  the  sake  of 
appearance. 

Let  us  assume  that  in  our  example  we  use  a  propeller  shaft 
tube  of  2  inches  outside  diameter  and  one-eighth  inch  thickness 
of  wall.  At  25,000  pounds  per  square  inch  this  will  sustain 
a  bending  moment  of 


32X2 

This  is  the  maximum  bending  moment  at  a  distance 

8>I17  =  17  inches  (aptr.) 

480 

from  the  support  and  the  remaining  length  of  the  tube,  there- 
fore, should  be  reinforced. 


268 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


The  practice  of  taking  both  the  driving  thrust  and  torque  re- 
action on  the  chassis  springs,  or  using  what  is  known  as  the 
Hotchkiss  drive,  is  now  quite  prevalent  in  both  pleasure  car 
and  truck  work. 

Torque  Tube  Supports— The  axle  tube  may  either  take  up 
Doth  the  torque  and  the  forward  thrust  on  the  rear  axle 
housing,  or  it  may  take  up  only  the  former,  and  the  method 
of  supporting  its  forward  end  varies  accordingly.  Fig.  172 
illustrates  a  construction  in  which  only  the  torque  is  taken 
up  by  the  tube,  the  forward  end  of  the  latter  riding  on  the 
propeller  shaft  through  the  intermediary  of  an  anti-friction 
bearing.  The  forward  end  of  the  propeller  shaft  is  supported 
by  the  universal  joint  which  is  secured  to  the  rear  end  of  the 
change  gear  primary  shaft.  A  disadvantage  of  this  construc- 
tion is  that  the  torque  reaction  has  to  be  taken  through  the 


FIG.  172. — TORQUE  TUBE  RIDING  ON.  PROPELLER  SHAFT. 

universal  joint  bearings.  The  pressure  due  to  the  torque 
reaction  also  comes  on  the  rear  bearing  of  the  change  gear 
box,  but  this  is  not  an  unmitigated  evil,  since  the  torque  re- 
action is  directed  perpendicularly  upward,  whereas  the  gear 
load  on  this  bearing  when  either  of  the  lower  gears  is  in 
operation  is  directed  almost  perpendicularly  downward,  hence 
the  torque  reaction  partly  neutralizes  the  gear  load.  Of 
course,  with  the  direct  drive  in  operation,  there  is  no  gear 
load  on  the  rear  bearing,  the  only  load  on  it  being  that  due 
to  the  torque  reaction,  and  since  this  is  always  far  below 
the  rated  capacity  of  the  bearing  there  is  no  serious  disad- 
vantage in  this. 

A  second  method  of  supporting  the  forward  end  of  the 
torque  tube  is  by  means  of  a  fork  hinged  to  a  cross  member 
of  the  frame  or  to  the  change  gear  box,  as  shown  in  Fig.  173. 
In  order  that  the  rear  axle  may  be  able  to  move  freely  in  the 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


269 


vertical  plane,  as  required  by  road  unevennesses,  the  fork 
must  swivel  on  the  front  end  of  the  torque  tube.  The  joints 
of  the  fork  and  the  abutting  surfaces  of  its  hub  should  be 
liberal  in  size  and  provided  with  means  for  lubrication.  The 
fork  is  usually  drop  forged,  and  its  arms  are  made  of  T-section. 
The  axis  of  the  hinged  joint  should  coincide  with  the  axis  of  the 
universal  joint  so  that  the  propeller  shaft  will  always  be  concentric 
with  the  torque  tube. 

A  third  method  of  supporting  the  forward  end  of  the  torque 
tube  is  by  means  of  a  spherical  joint  which  generally  also  forms 


FIG.  173. — FORKED  SUPPORT  OF  TORQUE  TUBE. 

a  protecting  housing  for  the  universal  joint  in  the  propeller  shaft 
As  shown  in  Fig.  174,  an  acorn-shaped  housing  is  bolted  to  the 
rear  of  the  change  gear  case  and  also  to  a  cross-member  of  the 
frame  which  is  of  special  shape,  with  a  hole  at  the  centre  for  the 
propeller  shaft  and  torque  tube  to  pass  through.  The  rear  end  of 
this  housing  is  turned  off  spherically  to  form  a  seat  for  a  spherical 
flange  formed  on  the  forward  end  of  a  sleeve  secured  to  the 
forward  end  of  the  torque  tube.  A  ring  with  a  spherical  bearing 
surface  is  bolted  to  the  frame  cross-member  in  such  a  manner  that 
the  spherical  portion  secured  to  the  torque  tube  works  freely  be- 


270 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


tween  the  two  parts  with  spherical  surfaces  secured  to  the  frame. 
A  leather  boot  or  a  packing  ring  has  to  be  provided  to  protect  the 
outer  working  surface  from  dust  and  grit.  The  universal  joint 
is  located  centrally  within  the  spherical  joint  and  the  forward 
end  of  the  propeller  shaft  is  generally  supported  in  a  ball  bearing, 
though  some  axles  have  recently  been  designed  which  do  away 
with  this  forward  bearing,  relying  on  the  universal  joint  for 
"steadying"  the  forward  end  of  the  shaft.  This  type  of  connec- 


FIG.  174.— SPHERICAL  SUPPORT  OF  TORQUE  TUBE. 

tion  between  the  frame  and  the  rear  axle  takes  up  frame  thrust 
in  both  directions  (driving  and  braking)  as  well  as  torsion,  and 
makes  for  a  very  substantial  construction. 

Effect  of  Spring  Play  on  Drive— In  Fig.  175  is  shown  a 
shaft  and  bevel  gear  drive  with  a  single  universal  joint  and 
a  torque  tube  surrounding  the  propeller  shaft.  The  forward 
end  of  the  propeller  shaft  is  shown  in  its  highest  position, 
22  inches  above  the  ground.  In  Fig.  176  the  same  drive  is 
shown  with  the  forward  end  of  the  propeller  shaft  in  its  low- 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


271 


*st  position,  16  inches  above  the  ground.  A  relative  change 
in  position  of  axle  and  frame  occurs  very  suddenly  when  the 
rear  wheels  strike  a  waterbar,  for  instance.  As  the  springs 
compress  the  forward  end  of  the  propeller  shaft  drops  sub- 
stantially in  an  arc  of  a  circle,  and  this  angular  motion  of 
the  propeller  shaft  around  the  rear  axle  axis  entails  a  corre- 
sponding rotary  motion  of  either  the  bevel  gear  or  the  bevel 
pinion.  That  is,  the  bevel  gear,  and  consequently  the  pair  of 
road  wheels,  will  move  around  their  common  axis  through 
an  angle  equal  to  that  described  by  the  propeller  shaft  or 
the  bevel  pinion,  or  the  engine  crankshaft  will  turn  around 
its  axis  through  an  angle  equal  to  the  product  of  the  angle 


FIG.  175. 

described  by  the  propeller  shaft  by  the  ratio  of  the  num- 
ber of  bevel  gear  teeth  to  the  number  of  bevel  pinion 
teeth.  In  the  illustration  the  horizontal  distance  between  the 
axle  centre  and  the  forward  end  of  the  propeller  shaft  is 
28  inches.  With  the  springs  compressed  the  propeller  shaft 
occupies  a  horizontal  position,  while  with  the  springs  ex- 
tended it  makes  an  angle  with  the  horizontal  whose  sine  is 

22  —  16 
-^-=0.214, 

viz.,  about  12^  degrees.  With  a  bevel  gear  ratio  of  3:1,  this 
corresponds  to  an  angular  motion  of  Z7l/2  degrees  of  the 
bevel  pinion.  Therefore,  in  the  design  shown  in  Figs.  175 


272 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


and  176,  if  the  frame  suddenly  drops  6  inches  relatively  to 
the  axle,  either  the  road  wheels  will  have  to  accelerate  so  as 
to  move  through  an  extra  angular  distance  of  12*/2  degrees 
during  the  short  space  of  time  that  the  compression  of  the 
springs  takes  place,  or  else  the  engine  has  to  slow  up  so  its 
crankshaft  will  turn  through  37^  degrees  less  than  normally 
during  this  period.  Both  changes  in  motion  are  opposed  by 
the  inertias  of  the  respective  moving  parts,  and  in  reality 
the  car  will  be  slightly  accelerated  and  the  engine  retarded 
by  the  compression  of  the  springs.  Preferably  the  play  of 
the  springs  should  have  absolutely  no  effect  on  the  motion 


FIG.  176. 

of  the  car  and  the  engine,  for  then  the  springs  would  act  most 
freely  and  the  transmission  parts  would  not  be  subject  to  shocks 
due  to  this  cause. 

In  Figs.  175  and  176  the  propeller  shaft  is  unusually  short, 
which  exaggerates  the  influence  of  spring  play  on  the  uniformity 
of  transmission.  The  designer's  aim  always  should  be  to  make 
the  propeller  shaft  as  long  as  possible,  especially  if  only  a  single 
universal  is  used.  If  the  shaft  is  twice  as  long  as  shown  in  the 
cuts — which  is  not  uncommon — the  speed  fluctuations  will  be 
almost  halved. 

When  two  universal  joints  are  used  a  torque  rod  is  usually 
employed  instead  of  a  torque  tube  concentric  with  the  pro- 
peller shaft.  By  supporting  the  front  end  of  the  torque  rod 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


273 


between  springs  from  the  frame  cross  member,  the  shock  on 
the  transmission  members  due  to  a  sudden  drop  of  the  frame 
is  lessened.  The  reason  why  this  is  so  is  immediately  ap- 
parent, because,  on  account  of  the  spring  suspension  of  the 
torque  rod,  the  forward  end  of  the  latter  need  not  drop  as 
much  as  the  frame. 

The  condition  insuring  that  there  shall  be  no  effect  on  the 
uniformity  of  the  drive  is  that  the  angle  of  the  pinion  axis 
with  the  ground  plane  remain  constant.  This  end  can  be 
attained  very  nearly  by  connecting  the  axle  housing  to  the 
frame  by  means  of  a  pair  of  parallel  links,  as  shown  in  Fig. 
177.  If  the  two  links  are  of  absolutely  the  same  length  and 


FIG.  177. 

the  front  and  rear  points  of  linkage  are  the  same  distance 
apart,  then  the  angle  made  by  the  axis  of  the  bevel  pinion 
with  the  plane  of  the  frame  will  remain  absolutely  constant. 
However,  this  does  not  quite  meet  the  above  mentioned  re- 
quirement that  the  pinion  axis  has  to  remain  at  the  same 
angle  with  the  ground  plane,  since  if  only  the  rear  springs 
compress  the  angle  of  the  frame  plane  with  the  ground  plane 
changes.  For  instance,  suppose  that  when  the  springs  are 
extended  both  the  frame  and  the  pinion  axis  are  absolutely 
horizontal.  Then  when  the  rear  springs  are  compressed  the 
frame  will  slant  toward  the  rear  and  so  will  the  pinion  axis. 
Since  the  pinion  axis  always  intersects  the  rear  axle  axis  it 
means  that  the  pinion  has  moved  slightly  upward,  thus 


274  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

causing  a  slight  retardation  in  the  speed  of  the  car  or  an 
acceleration  in  the  speed  .of  the  motor.  This  effect  is  really  so 
slight  as  to  be  negligible,  but  it  can  be  entirely  eliminated  by 
making  the  upper  rod  longer  or  placing  the  rear  pivots 
farther  apart  than  the  front  pivots.  This  linkage  is  used  by 
Deasy  and  Lanchester  in  England,  among  others. 

Some  experiments  by  means  of  models  on  the  effect  of 
spring  play  on  bevel  gear  drives  were  made  several  years 
ago  by  S.  Gerster,  of  Courbevoie,  France,  and  were  reported 
in  THE  HORSELESS  AGE  of  December  15,  1909.  The  experi- 
mental apparatus  consisted  of  the  rear  portion  of  a  vehicle 
frame,  a  set  of  rear  springs,  an  axle,  a  pair  of  wheels  and 
the  bevel  gear  drive.  The  rear  wheels  were  fixed  to  a  wooden 
base,  and  double  cords  were  attached  to  the  frame  at  three 
points,  these  cords  passing  through  holes  in  a  wooden  base 
and  over  pulleys  on  the  under  side  of  the  base,  and  were 
connected  to  a  single  pull  rod  underneath,  by  pulling  on  which 
the  frame  could  be  lowered  relatively  to  the  base  a  distance 
of  6  inches.  On  a  cross-member  of  the  frame  was  mounted 
a  dial,  and  to  the  forward  end  of  the  propeller  shaft  directly 
in  front  of  this  dial  was  secured  a  pointer,  which  latter  moved 
over  a  scale  on  the  dial  graduated  in  degrees.  Mr.  Gerster 
constructed  models  of  this  description  with  all  of  the  differ- 
ent types  of  axle  linkage  in  common  use.  The  length  of  the 
propeller  shaft  was  the  same  in  every  case.  When  the  frame 
was  depressed  6  inches  by  pulling  on,  the  cords  the  pointer 
would  move  the  following  angular  distances  over  the  dial 
with  different  linkages:  Degrees 

Torque  tube  hinged  to  cross  member  of  frame 54 

Triangular  torque  tube  spring  supported  from  frame  and  radius  rods 

at  the  sides 31 

Only  connection  through  three-quarter  elliptic  springs 5 

Parallel  links;  top  one  somewhat  shorter  than  lower  ones — less  than..  i 

Torque  Rods — In  American  practice  three  general  designs  of 
torque  rods  are  met  with,  viz.,  rods  of  round  section,  either 
solid  or  hollow,  which  are  fitted  into  a  socket  formed  in- 
tegral with  the  driving  gear  housing,  as  shown  at  A,  Fig.  178; 
pressed  steel  rods  of  channel  section,  as  shown  at  B,  or  tri- 
angular rods,  as  shown  at  C.  There  are  also  some  examples 
of  malleable  iron  torque  rods  of  I  section,  pressed  steel  torque 
rods  of  I  section  made  by  riveting  two  channels  together 
back  to  back,  and  wooden  torque  bars. 

A  tubular  torque  rod,  of  course,  is  preferable  to  a  solid 
round  one,  since  for  equal  strength  it  is  lighter.  The  reason 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


275 


that  solid  rods  are,  nevertheless,  used  to  quite  an  extent  is 
undoubtedly  that  it  is  much  easier  to  taper  the  solid  rod  so 
the  strength  of  the  section  at  every  point  is  proportional  to 
the  stress  at  that  point.  Tubular  rods  can  be  tapered  only 
with  difficulty,  and  the  common  plan  is  to  use  tubes  of 
uniform  diameter  and  insert  one  or  two  reinforcing  tubes 
from  the  rear  end.  The  forward  ends  of  these  reinforcing 
tubes  should  either  be  tapered  out  or  else  cut  off  at  an 
angle  so  as  to  avoid  a  sudden  change  in  the  strength  of  the 
section. 


C 


FIG.  178.— TYPES  OF  TORQUE  RODS. 

Pressed  steel  and  triangular  torque  rods  are  frequently 
connected  to  the  driving  axle  housing  by  means  of  a  vertical 
hinge  joint,  as  shown  at  B,  Fig.  178.  This  obviates  undue 
strains  on  the  casing  and  torque  rods  in  the  case  of  severe 
lateral  shocks  on  the  rear  system,  as  in  striking  a  curb  in 
skidding.  It  will  be  seen  that  in  the  construction  shown  at 
B  a  drop  forged  or  cast  fork  is  riveted  to  the  pressed  steel 
member  for  making  the  joint  to  the  driving  gear  housing. 
In  other  constructions  the  housing  is  formed  with  a  flat  to 


276 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


which  the  pressed  steel  member  is  bolted  directly.  In  the 
case  of  pressed  steel  members  some  of  the  material  of  the 
web  of  the  channel  is  generally  removed,  as  shown  in  Fig.  178, 
thus  eliminating  weight  without  materially  reducing  the 
strength,  since  the  material  near  the  neutral  axis  is  under 
little  strain. 

The  advantage  of  the  triangular  torque  rod  is  that  its  mem- 
bers work  under  tension  and  compression  instead  of  under 
bending  stresses.  The  individual  members  are  generally  tubu- 


FIG.  179.  FIG.  180. 

SPRING  CUSHION  SUPPORT  FOR  FORWARD  END  OF  TORQUE  ROD. 

lar.  Often  they  are  secured  to  the  driving  gear  housing  by 
two  of  the  bolts  holding  the  halves  of  the  housing  together, 
though  occasionally  they  are  secured  thereto  by  special  bolts, 
as  shown  in  Fig.  178. 

Two  common  methods  of  supporting  the  forward  end  of 
the  torque  rod  from  the  frame  are  illustrated  in  Figs.  179 
and  180,  respectively.  From  a  bracket  riveted  to  a  frame 
cross-member  depends  a  freely  swiveled  cylindrical  spring 
housing  containing  two  coiled  springs  between  which  the  for- 
ward end  of  the  torque  rod  is  cushioned.  The  end  of  the 
rod  is  made  either  in  the  form  of  an  eye,  as  in  Fig.  179,  or 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


277 


in  the  form  of  a  ball,  as  in  Fig.  180,  in  which  latter  case  it 
is  held  between  two  spring  plates  with  part  spherical  de- 
pressions 

The  simplest  construction  consists  in  a  simple  link  con- 
nection between  the  frame  bracket  and  the  torque  rod,  as 
shown  in  Fig.  181.  This,  of  course,  does  not  afford  the 
cushioning  effect  that  the  spring  support  does.  In  order 
to  obtain  some  of  this  cushioning  effect  without  the  use  of 
springs,  some  foreign  manufacturers  of  motor  trucks  use 
wooden  torque  bars. 


FIG.   181. — LINK  SUPPORT  OF  TORQUE  ROD. 

The  stresses  in  torque  rods  and  the  sections  required  are 
calculated  the  same  as  in  the  case  of  torque  tubes. 

Diagonal  Brace  Rods — The  tendency  of  the  rear  axle  to  be 
thrown  out  of  alignment  with  the  frame  when  one  of  the 
driving  wheels  strikes  a  road  obstruction  has  already  been 
referred  to.  Some  designs  of  axle  housing,  as,  for  instance, 
the  Fiat  pressed  steel  housing,  are  amply  strong  to  withstand 
these  stresses,  but  others  require  radius  rods  to  be  fitted 
between  the  axle  housing  and  the  side  frames,  or  diagonal 
brace  rods  between  the  spring  seats  or  brake  supports  on 
the  axle  housing  and  the  forward  end  of  the  torque  tube.  A 
typical  rear  axle  construction  with  diagonal  brace  rods  is 


278 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


shown  in  Fig.  182.  The  braces  are  made  either  tubular  or 
solid,  and  either  hinged  at  both  ends  or  at  the  rear  end  only, 
and  screwed  into  the  fitting  at  the  forward  end. 

The  spring  seats  and  brake  supports  also  are  integral  parts 
of  the  rear  axle,  but  they  will  be  discussed  under  the  headings 
of  springs  and  brakes,  respectively. 


ID. 


FIG.   182.— DIAGONAL  BRACE  RODS. 


Bevel  Gear  Efficiency—Some  tests  of  the  efficiency  of  trans- 
mission in  bevel  gear  driven  rear  axles  were  made  several 
years  ago  by  the  H.  H.  Franklin  Mfg.  Co.,  Syracuse,  N.  Y., 
and  were  reported  by  G.  Everett  Quick  in  THE  HORSELESS 
AGE  of  February  12,  1908.  The  tests  were  conducted  in  sub- 
stantially the  same  manner  as  those  of  change  gears,  already 
referred  to,  except  that  two  absorption  dynamometers  were 
used,  one  connected  to  either  rear  axle  shaft,  and  the  differ- 
ential was  locked.  Fig.  183  gives  the  results  of  tests  of  a 
full  floating  axle.  The  bevel  gears  had  five  pitch  14^2  degree 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


279 


involute  teeth  and  gave  a  gear  ratio  of  15:52.  They  were 
cut  from  3l/2  per  cent,  nickel  steel  blanks,  case  hardened,  the 
hardened  surfaces  of  the  teeth  being  polished  by  running  the 
gears  together  in  a  mixture  of  emery  and  oil.  The  length 
of  face  was  \l/2  inches.  The  axle  had  been  run  for  about 
3,000  miles  previous  to  the  test.  It  will  be  seen  from  the 
diagram  that  the  maximum  efficiency  is  about  97  per  cent., 
and  the  efficiency  is  above  95  per  cent,  for  a  considerable 
range  in  horse  power  transmitted  and  speed  of  revolution.. 
During  the  test  the  axle  gears  were  run  in  a  bath  of  graphite 
and  oil.  The  losses  shown  by  the  diagram  include  both  gear 
and  bearing  losses,  but  the  latter  are  very  small,  as  all  bear- 
ings were  radial  ball  or  ball  thrust  bearings.  A  semi-floating 


X5 


68/0       fig       '4       16       /8 
Morse  Power    Delivered  to  Pinion 


FIG.  183. — EFFICIENCY  OF  BEVEL  GEAR  DRIVEN,  FULL  FLOATING 
REAR  AXLE. 


axle  was  also  tested  and  showed  substantially  the  same  max- 
imum efficiency,  but  a  slightly  higher  efficiency  at  small  loads. 
Critical  Speed  of  Shafts. — Not  long  after  the  shaft  drive 
became  popular  trouble  began  to  develop  from  inordinate  vibra- 
tion and  resulting  permanent  bending  or  breaking  of  the  pro- 
peller shafts  at  certain  critical  speeds,  especially  on  cars  with 
unit  power  plants  or  transmission  axles,  which  necessitate  the 
use  of  exceptionally  long  propeller  shafts.  The  occurrence 
of  such  trouble  was  first  brought  to  public  attention  by  the 
provision  in  certain  cars  of  intermediate  bearings  on  the  pro- 
peller shaft.  The  trouble  may  have  seemed  mysterious  at 
first,  but  the  phenomenon  was  not  entirely  newx  as  similar 
trouble  had  been  experienced  with  steam  turbines  some  years 
previously,  and  a  mathematical  explanation  of  the  phenomenon 


280 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


of  critical  speeds  of  revolving  shafts  had  already  been  given. 
The  explanation  is,  briefly,  as  follows : 

In  spite  of  careful  workmanship  the  center  of  mass  of  the 
revolving  shaft  will  never  lie  exactly  in  the  axis  of  revolution. 
Owing  to  the  eccentricity  of  the  center  of  mass  an  unbalanced 
centrifugal  force  is  produced  which  causes  the  shaft  to  vibrate. 
The  phenomenon  is  the  more  pronounced  if  the  shaft  carries  a 
heavy  disc  at  the  middle  of  its  length,  whose  center  of  mass 
lies  outside  the  axis  of  rotation.  (See  Fig.  184.)  Let  the  center 
of  mass  be  at  a  distance  d  from  the  axis  of  revolution  of  the 
shaft.  Under  the  influence  of  centrifugal  force  the  shaft  at  the 
middle  of  its  length  will  deflect  the  distance  y  from  its  neutral 
position.  When  thus  deflected  there  will  also  be  an  unbalanced 


FIG.  184. — SHAFT  CARRYING  A  CENTRAL  UNBALANCED  Disc. 


centrifugal  force  acting  on  the  mass  of  the  shaft,  which  will  add 
to  the  centrifugal  force  acting  on  the  mass  of  the  disc,  but  for 
the  present  purpose  it  is  permissible  to  neglect  the  former.  De- 
noting the  mass  of  the  disc  by  m,  the  centrifugal  force  is  ex- 
pressed by 

F  =  m  (y  +  d)  «», 
o>  being  the  angular  speed  in  radians  per  second. 

This  force  is  balanced  by  the  elastic  force  of  the  shaft  which 
is  proportional  to  the  deflection  and  may,  therefore,  be  repre- 
sented by 

Fe  =  a  y. 
Hence 

m  (y  +  e)  ^  =  a  y 
from  which  it  follows  that 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  281 

and 

me  o>2 

a  —  m  0? 

When  a  =  m  ^  the  deflection  becomes  infinite ;  that  is,  unless 
the  vibration  of  the  shaft  is  limited  by  bearings  or  guards,  the 
shaft  will  break.  This,  therefore,  is  the  condition  defining  the 
critical  speed.  There  is  one  other  exception  in  addition  to 
that  noted  above  which  would  preclude  breaking  of  the  shaft, 
and  that  is  that  the  speed  of  revolution  of  the  shaft  varies  so 
rapidly  that  it  remains  near  the  critical  speed  an  insufficient 
length  of  time  to  permit  of  a  dangerous  vibration  being  attained. 
Since  the  equation  defining  the  critical  speed  is 

a  =  m  w2 
the  value  of  the  critical  speed  is  evidently 


m 

In  order  that  the  centrifugal  force  may  be  expressed  in  pounds 
(the  angular  speed  w  being  given  in  radians  per  second)  the 
linear  dimensions  must  be  given  in  terms  of  the  foot,  and  a 
then  is  the  force  necessary  to  deflect  the  shaft  one  foot  at  the 
middle  of  its  length. 

Analysis  of  Critical  Speeds. — Now  consider  a  section  dx  of 
a  freely  supported  shaft  carrying  only  its  own  weight.  When 
the  shaft  rotates  the  shaft  section  dx  is  under  the  influence  of 
two  external  forces,  the  force  of  gravity  and  centrifugal  force. 
With  the  shaft  proportions  found  in  practice  the  former  has 
no  appreciable  bending  effect  and  may  be  neglected.  The  cen- 
trifugal force  puts  a  load  on  the  shaft  which  revolves  with  it 
and  subjects  it  to  shear  and  bending  stresses.  These  latter  can 
be  determined  by  means  of  the  theory  of  beams,  the  shaft  being 
equivalent  to  a  simple  beam  supported  at  both  ends.  When 
the  shaft  is  in  equilibrium  the  external  (centrifugal)  and 
internal  (elastic)  forces  must  neutralize  each  other  in  every 
plane. 

Let  the  shear  at  the  two  sides  of  the  infinitesimal  section 
dx  of  the  shaft  be  denoted  by  S  and  S'  respectively.  The  cen- 
trifugal force  on  the  section  dx  is  proportional  to  the  length 
dx  and  may  be  represented  by  p  dx,  where  p  is  the  centrifugal 
force  per  unit  length.  Then,  since  there  must  be  equilibrium  in 
the  vertical  plane  (see  Fig.  185) 

S'  —  S  +  p  dx  =  O 


282 
But 

hence 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 
S'  —  S  =  d  S 

ds 


Also,   taking   moments   around   the    center    of   gravity    of    the 
section  dx 

dx  dx 

Mr  —  M  —  S'  --  S  -  =  O 
2  2 


FIG.    185. — DIAGRAM   CF   CENTRIFUGAL  AND  ELASTIC   FORCES. 


and  since 
we  have 


—  M  =  dM 


S'  +  S 
dM  = • dx  =  S  dx 


This  relation  can  now  be  combined  with  the  equation  of  the 
elastic  curve  of  a  beam,  viz., 

dzy  -  M 

dx2  El 

the  minus  sign  being  used  here  to  correspond  with  the  designa- 
tions in  the  cut. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  283 

Since 

dM 

'  ^ 

dx 

dS  dzM                    d*y 

=  _  p  = =  _  £  I  - — 

dx  d.r                     dx' 
Hence 

<Ty 

p  =  E  I  -         =  m  <»*  (y  +  d) 
dx* 

The  general  integration  of  this  equation  gives 

y  =  a  e  cx  a'  e  —  cx  ~h  b  cos  ex  +  b'  sin  ex  —  d 
in  which 


IE 

and  e  is  the  base  of  the  natural  system  of  logarithms.  This 
equation  covers  all  possible  conditions  of  rotating  shafts,  and 
the  values  of  the  constants  a  a'  b  b'  depend  upon  the  conditions 
of  any  particular  case — whether  the  shaft  is  freely  supported 
or  rigidly  held  in  bearings,  supported  at  both  ends  or  at  one 
end  only,  etc. 

If  now  we  take  a  freely  supported  shaft  like  a  propeller  shaft 
with  universal  joints  at  both  ends,  and  if  we  measure  the  ab- 
scissas from  the  middle  of  length  of  the  shaft,  then  3;  must  be 
an  even  function  of  x,  in  order  that  the  same  value  for  y  may 
be  obtained  for  equal  positive  and  negative  values  of  x.  The 
third  term  of  the  above  equation  for  y  contains  a  cosine  and  the 
value  of  the  cosine  is  the  same  for  a  positive  and  negative  angle 
of  equal  magnitude.  The  sines  of  positive  and  negative  angles 
are  alike  but  opposite  in  sign.  A  change  in  the  sign  of  x  would 
not  give  the  same  value  of  opposite  signs  for  each  of  the  first 
two  terms.  Consequently  variations  in  the  first  two  terms  due  to 
a  change  in  the  sign  of  x  could  not  be  compensated  for  by  a 
corresponding  variation  in  the  fourth  term.  The  conclusion  to 
be  drawn  is  that  when  x  changes  sign  there  is  no  variation  in 
the  sum  of  the  first  two  terms,  and  no  variation  in  the  value  of 
the  fourth  term.  From  this  it  follows  that 

a  =  a'  and  b'  =  o 
This  gives  us 

y  =  a  (c  cx  +  c  —  cx)  +  b  cos  cx  —  d 
Nowv  when  x  =  I  or  —  / 


284  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

d2y  —M 


dS  El 

because  M  =  o. 

Under  these  conditions 


Hence 


-  =  a  (e  c  »  +  e  )  —  b  cos  cl  =  o 

dxz 


a  (e  c  l  +  c~       )  =  b  cos  cl 


Substituting   in   the   above   equation    for  y   and   remembering 
that  when  x  =  /,  y  =  o, 

2a  (e  «*  +  e~~  '')  =  d 


a  = 


2  (e  "  +   c~~        ) 
Also 

2b  cos  cl  =  d 

d 

b  =  

2  cos  cl 

When  cos  cl  is  zero  the  value  of  b,  and  consequently  the  value 
of  y,  the  deflection  becomes  infinite,  and  the  shaft  runs  at  the 
critical  speed.  This  is  the  case  when  cl  =  n/2,  3  V2,  5  V2, 
etc.  There  are,  therefore,  a  number  of  critical  speeds.  Now, 
inserting  the  value  of  c  in  the  equation  for  b  and  equating  the 
latter  to  the  smallest  angle  corresponding  to  a  critical  speed  we 
get 


IE 


IE  16 


16m/4 
in  which 

w  is  the  angular  speed  in  radians  per  second 
/,  the  moment  of  inertia  of  the  shaft  section 
E,  the  modulus  of  elasticity 
m,  the  mass  of  the  shaft  per  inch  length 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  285 

/,  half  the  length  of  the  shaft  in  inches. 

The  mass  of  the  shaft  section  is  equal  to  its  weight  divided 
by  the  constant  of  gravity,  but  in  this  case,  as  the  units  used 
must  be  the  same  throughout  and  as  the  shaft  diameter  and 
shaft  length  are  expressed  in  inches,  we  must  express  the  accel- 
eration of  gravity  in  inches  per  second  per  second,  instead  of 
feet  per  second  per  second.  Therefore 

g  =  32.16  X  12  =  386. 

From  the  equation  for  w  the  critical  speed  of  any  shaft  can 
be  calculated,  but  this  equation  is  in  a  rather  inconvenient  form ; 
it  would  be  much  preferable  if  the  critical  speed  n  in  revolu- 
tions per  minute  could  be  calculated  directly  from  the  dimensions 
of  the  shaft,  and  this  can  be  done  if  the  equation  is  suitably 
transformed. 

We  have 


60 
co2  =  - 


3,600 

64 
E  =  30,000,000 

W 
m  =  — 

386 

W  = X  0.28  =  0.07 

4 
Hence 

A  A7  TT  slz  —  j2 

U.U/  «  a  •  «  a 


386  5,500 


V 

**  =  — 
16 

L  being  the  whole  length  of  the  shaft  between  supports. 


286  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

Inserting  these  values  in  the  equation  for  w2  we  get 


*       d*  5,500        16 

=  _  x  —  X  30,000,000  X  -  X  — 


,, 

3,600        16      64  7r<f 

which  when  simplified  gives 


w2  =  2,320,000,000,000  - 

L4 
Therefore 

vd  d 

n  =  1,520,000  -  =  4,800,000  — 

L2  L2 

This  equation  applies  to  solid  round  shafts.  Equations  for 
shafts  with  other  sections  can  easily  be  derived  by  means  of 
the  equation  for  w2.  It  will  be  seen  that  this  value  varies  di- 
rectly as  the  moment  of  inertia  of  the  section  and  inversely  as 
the  mass  per  unit  length,  all  the  other  factors  in  the  equation 
being  independent  of  the  section.  Therefore 


m 

But  m,  the  mass  per  unit  length,  is  directly  proportional  to 
the  area  of  the  section,  which  we  may  denote  by  A.  Conse- 
quently 


or  as  the  least  radius  of  gyration  of  the  shaft  section.     For  a 
solid  circle  of  diameter  d 

17      \~^7*      4~~      IT    d 

V^  3"V  64        »</"  M6~  4 

For  a  hollow  circle  of  outside  diameter  d  and  inside  diameter 
d* 


4  /d'  +  A1 

d2  -  df)  *V       16~~ 


64 
For  a  solid  square  shaft  whose  side  measures  d, 


* 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE.  287 

Hence  a  tubular  shaft  of  outside  diameter  d  and  inside  diameter 
di  has  a  higher  critical  speed  than  a  solid  round  shaft,  the  ratio 
between  the  two  critical  speeds  being 


2  + 


d 

and  a  solid  square  shaft  whose  sides  measure  d  has  a  higher  crit- 
ical speed  than  a  solid  round  shaft  of  diameter  d,  the  ratio  of 
critical  speeds  being 

d  d 

--  -*-.—  =  1.155 
3.46         4 

Hence,  we  have  the  following  formulae  -for  the  critical  speeds 
of  other  than  solid  round  shafts  : 
For  a  round  tubular  shaft, 

V  d~  +  di2 
nc  =  4,800,000      -  L!!L 

L2 
For  a  solid  square  shaft  whose  sides  measure  d 

d 

nc  =  5,520,000  — 
L2 

Agreement  with  Practical  Observations.—  It  has  been  found 
in  practice  that  the  actual  critical  speed  is  always  somewhat 
lower  than  the  calculated  value.  For  instance,  Stodola  in 
'The  Steam  Turbine"  gives  several  examples  of  tests  for  criti- 
cal speeds  of  shafts.  In  five  of  these  tests  the  critical  speed 
was  found  to  be  6  per  cent.,  8  per  cent.,  9  per  cent.,  13  per  cent. 
and  14  per  cent:  below  the  calculated  value.  This  discrepancy 
is  undoubtedly  due  to  the  fact  that  the  points  of  support  are  not 
rigid.  An  automobile  propeller  shaft  when  running  at  high 
speed  will  whirl  in  the  same  way  as  a  heavy  rope  which  is 
being  swung  around  by  two  persons.  If  they  cease  their  whirl- 
ing effort  their  hands  will  nevertheless  be  carried  around  in  a 
circle,  and  so  with  the  propeller  shaft  supports.  The  latter 
consist  of  the  universal  joints  which  are  fitted  to  shafts  over- 
hanging their  bearings,  and  under  the  influence  of  the  cen- 
trifugal force  on  the  propeller  shaft  these  short  shafts  will  bend 
in  the  same  plane  as  the  propeller  shaft,  thus  virtually  increas- 
ing the  distance  between  supports.  The  effect  depends, 
of  course,  upon  the  relative  stiffness  and  amount  of  overhang 
of  the  connected  shafts,  but  it  has  been  found  that  if  the  cal- 


288  BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 

culated  critical  speed  is  not  approached  closer  than  within  15 
per  cent,  a  sufficient  degree  of  safety  is  allowed  in  ordinary  con- 
structions. 

The  critical  speed  above  discussed  is  the  lowest  critical  speed. 
There  is  an  endless  number  of  higher  critical  speeds,  but  these 
are  of  no  interest  from  a  practical  standpoint,  as  the  shaft,  to 
be  safe,  must  be  made  of  such  dimensions  that  its  lowest  criti- 
cal speed  is  never  attained  in  practice. 

The  following'  table  gives  the  critical  speeds  of  solid  round 
steel  shafts  of  different  diameters  and  lengths : 

CRITICAL  SPEEDS    (R.P.M.)    OF  FREELY   SUPPORTED 
SOLID  STEEL  SHAFTS. 


d     L 

=  35" 

40" 

45" 

50" 

55" 

60" 

65" 

70" 

1 

3,915 

3,000 

2,370 

1.920 

1,585 

1,335 

1,135 

980 

1%" 

4,400 

3,375 

2,660 

2,160 

1,785 

1,500 

1,275 

1,105 

W 

4,900 

3,750 

2,960 

2,400 

1,985 

1,670 

1,420 

1,225 

1%" 

5,400 

4,125 

3,260 

2,640 

2,180 

1,835 

1,560 

1,350 

iy2" 

5,880 

4,500 

3,550 

2,880 

2,380 

2,000 

1,705 

1,470 

i%" 

6,380 

4,875 

3,850 

3,120 

2,580 

2,170 

1,845 

1,595 

\y4" 

6,860 

5,250 

4,150 

3,360 

2,775 

2,340 

1,990 

1,715 

Shafts  Fixed  at  Ends. — The  case  of  a  shaft  fixed  at  both  ends 
is  not  so  common  in  automobile  practice,  but  may  occur,  as,  for 
instance,  when  the  propeller  shaft  is  surrounded  by  a  torque 
tube  mounted  on  roller  bearings  at  both  ends.  A  shaft  so  sup- 
ported when  under  the  influence  of  centrifugal  force  will  form 
a  compound  curve,  and  as  the  distance  between  inflection  points 
is  then  so  much  less,  a  greater  centrifugal  force  is  required  to 
cause  the  deflection,  consequently  the  critical  speed  is  higher.  An 
analysis  of  the  problem  shows  that  the  critical  speed  of  a  solid 
round  steel  shaft  of  length  L,  fixed  at  both  ends,  is : 

d 

nc  =  11,240,000  — , 
L- 
and  the  critical  speed  of  a  hollow  steel  shaft  fixed  at  both  ends, 


I  d*  +  d? 

no  =  11, 240,000  \_ 


L2 

Manufacture  of  Rear  Axles. — The  designs  of  rear  axles  differ 
widely,  and  as  a  result  there  is  great  divergence  in  the  methods  of 
manufacture,  since  the  manufacturing  processes  naturally  must 
be  adapted  to  the  design.  For  this  reason  it  is  not  possible  to  give 
more  than  a  very  general  description  of  rear  axle  manufacture  in 
this  work. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


289 


Among  the  most  important  parts  of  the  axle  are  the  bevel 
gear  and  its  pinion.  These  must  be  very  accurately  cut  in 
order  that  they  may  run  with  very  little  noise,  even  at  high 
car  speeds.  Besides,  the  cutting  of  bevel  gears  involves  much 
greater  difficulty  than  the  cutting  of  spur  gears.  The  stock- 
ing or  rough  cutting  can  be  done  by  means  of  a  formed 


T-I.  186. — STOCKING  BEVEL  GEARS. 


290 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


cutter  in  a  milling  machine  or  gear  cutter  of  similar  type,  as 
shown  in  Fig.  186,  but  the  finishing  should  preferably  be  done 
in  a  bevel  gear  planer,  as  this  insures  greater  accuracy.  The 
bevel  gears  must  also  be  case  hardened  or  oil  hardened,  and 
to  correct  the  defects  due  to  warping  when  the  gears  are 
quenched,  the  latter  are  often  run  together  in  a  special  fixture 
with  a  mixture  of  emery  and  oil.  Fig.  187  illustrates  the  process 
of  grinding  the  gears  in  the  plant  of  the  Timken-Detroit  Axle  Co. 
by  means  of  a  machine  developed  in  the  company's  own  shop. 


FIG.  187. — GRINDING-IN  OF  BEVEL  GEARS. 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


291 


The  bevel  pinion  and  gear  are  mounted  on  spindles  at  right 
angles  to  each  other.  The  spindle  on  which  the  pinion  is  mounted 
is  driven  by  belt  from  a  countershaft  and  the  other  spindle 
through  a  pair  of  accurately  cut  bevel  gears  of  the  same  ratio  as 
the  pair  to  be  ground.  The  driving  bevel  gears  are  so  adjusted 
as  to  run  without  back  lash,  and  are  enclosed  to  protect  them 
from  the  emery  powder  with  which  the  other  gears  are  ground  in. 


FIG.  188.— TURNING  UP  BEVEL  PINION  BLANK. 

In  bevel  gear  drives  employing  two  universal  joints  in  the  pro- 
peller shaft,  the  bevel  pinion  and  its  shaft  are  frequently  made 
integral,  and  Fig.  188  illustrates  a  time  saving  method  of  machin- 
ing up  such  blanks  in  a  Fay  lathe  made  by  the  Jones  &  Lamson 
Machine  Co.,  of  Springfield,  Vt.  Three  cutting  tools  are  used, 
of  which  one  is  carried  on  the  back  rest,  and  all  of  the  machining 
operations  are  performed  at  one  setting. 

As  a  rule,  there  are  a  great  many  machine  operations  to  be 
performed  on  the  driving  gear  housing,  such  as  boring  the 
holes  for  the  axle  tubes,  the  seats  for  bearings,  etc.  Fig. 
189  illustrates  the  method  of  boring  the  gear  carrier  of  a  Timken- 
Detroit  rear  axle.  In  this  part,  the  same  as  in  the  halves  of  a  cast 


292 


BEVEL  GEAR  DRIVE  AND  REAR  AXLE. 


driving  gear  housing,  there  are  a  number  of  concentric  holes  to  be 
bored,  and  a  turret  lathe  is  therefore  a  very  advantageous  tool. 
In  order  to  get  the  bores  for  the  axle  tube  and  for  the  propeller 
shaft  housing  absolutely  at  right  angles  with  each  other,  some 


FIG.  189. — BORING  GEAR  CARRIER  IN  VERTICAL  TURRET  LATHE. 

manufacturers  use  special  three  spindle  boring  machines,  one  of 
the  spindles  being  at  right  angles  to  the  other  two.  The  greatest 
accuracy  is  required  in  boring  the  seats  for  the  bearings. 


CHAPTER  X. 


THE  WORM  DRIVE. 

Transmission  of  power  by  worm  and  worm  wheel  in  an  auto- 
mobile originated  in  England,  where  it  is  used  for  both  pleasure 
and  commercial  vehicles.  More  than  a  score  of  British  manufac- 
turers of  pleasure  cars  fit  either  all  or  some  of  their  models  with 
worm  drives,  or  give  an  option  on  this  drive.  The  worm  drive 
has  also  secured  a  foothold  in  Germany  and  France  and  is  very 
largely  used  for  commercial  vehicle  drives  in  this  country. 

Up  to  about  twenty  years  ago  the  worm  and  wheel  were  con- 
sidered merely  a  means  for  transmitting  motion,  as  distinguished 
from  a  means  for  transmitting  power.  As  it  to  be  expected,  when 
the  teeth  are  not  very  accurately  cut  and  when  they  run  together 
dry  or  without  lubrication,  the  efficiency  of  the  gear  is  very  low 
and  its  wear  is  rapid.  Worm  gearing  was  first  developed  for 
commercial  power  transmission  purposes  in  connection  with  elec- 
tric motors.  These  were  the  first  high  speed  motors  to  come  into 
practical  use  and  high  reduction  ratios  were  required  in  many 
lines  of  application.  For  automobile  work  the  worm  gear  was 
first  taken  up  by  F.  W.  Lanchester  and  the  Dennis  Brothers  of 
England. 

Advantages  of  Worm  Drive. — The  worm  drive  is  at  its 
greatest  advantage  when  a  high  ratio  of  reduction  is  desired. 
With  a  bevel  gear  or  chain  drive  it  is  difficult  to  secure  a  gear 
ratio  of  more  than  5  to  1,  if  road  wheels  of  the  usual  size  are 
to  be  used,  and  in  types  of  vehicles  requiring  a  higher  reduction 
ratio,  including  nearly  all  types  of  commercial  vehicles  except 
those  shod  with  pneumatic  tires,  it  is  a  question  of  using  either 
the  worm  drive  or  a  double  reduction  drive  by  bevel  gears  and 
chains.  The  worm  drive  then  has  the  advantage  as  regards  sim- 
plicity of  construction.  Among  other  advantages  of  this  drive 
may  be  mentioned  its  absolutely  silent  operation  and  the  possi- 

293 


294  THE  WORM  DRIVE. 

bility  of  providing  a  very  wide  range  of  gear  ratios  without 
change  in  th2  distance  between  the  axes  of  worm  and  wheel 
or  in  adjacent  parts.  The  worm  drive  gives  a  symmetrical  rear 
axle  which  is  comparatively  easy  to  assemble. 

Theory  of  Worm  Gearing  —  The  worm  gear  as  applied  to 
automobile  driving  is  similar  to  a  helical  gear,  the  worm  being 
always  of  the  multiple  thread  type,  and  some  of  the  rules  of  heli- 
cal gearing  therefore  also  apply  to  worm  gear.  In  a  worm  and 
worm  wheel  the  gear  reduction  is  equal  to  the  quotient  of  the 
number  of  teeth  in  the  worm  wheel  by  the  number  of  threads 
in  the  worm.  The  lead  of  the  worm  is  the  distance  in  the  di- 
rection of  the  worm  axis  corresponding  to  one  complete  revo- 
lution of  the  worm  thread.  The  angle  of  lead  is  the  angle  made 
by  the  worm  thread  at  the  pitch  line  with  a  plane  perpen- 
dicular to  the  worm  axis  (also  the  angle  made  by  a  worm  wheel 
tooth  with  the  worm  wheel  axis).  In  connection  with  helical 
gears  it  is  the  custom  to  speak  of  the  angle  of  spiral,  which  is 
the  angle  made  by  an  element  of  the  gear  tooth  with  the  gear 
axis,  and  in  case  the  two  axes  are  at  right  angles  to  each  other 
(as  in  a  worm  and  wheel)  the  angles  of  spiral  for  the  two 
gears  together  make  a  right  angle.  In  a  worm  gear  the  angle 
of  lead  corresponds  to  the  angle  of  spiral  for  the  worm  wheel, 
while  the  complement  of  the  angle  of  lead  corresponds  to  the 
angle  of  spiral  for  the  worm. 

Following  are  definitions  of  some  terms  used  in  connection 
with  worm  gearing: 

Circular  pitch  _  Pitch  diameter  x  3.  1416 
(of  wheel)  ~~No.  of  teeth 

Axial  pitch  __  Lead 
(of  worm)       No.  of  threads 
Circular  pitch  of  wheel  =  Axial  pitch  of  worm. 
Normal  circular  pitch  =  Circular  pitch  x  cos  of  angle  of  lead. 

In  calculating  worms  and  worm  wheels  the  following  equation- 
may  be  used  : 

WORM 

Pitch  diameter  =  No.  of  threads  x  normal  circular  pitch 

3.  1416  x  sin  of  angle  of  lead. 

Lead  =  Pitch  diameter  x  3.1416  x  tan  of  angle  of  lead. 

2  X  axial  pitch 


Outside  diameter  =  pitch  diameter  + 

Normal  circular  pitch  =  —  -  .    ;. 

Normal  diametral  pitch. 


THE  WORM  DRIVE.  295 

WHEEL 

No.  of  teeth  X  normal  circular  pitch 
3.1416  X  cos  of  angle  of  lead. 

Pitch  diameter  X  3.1416 
e  tan  of  angle  of  lead. 

2  X  axial  pitch 
Throat  diameter  =  pitch  diameter  +  —     —  3         — 


The  centre  distance  or  distance  between  the  axes  of  worm  and 
wheel  is  equal  to  one-half  the  sum  of  the  two  pitch  diameters. 
Worm  and  wheel  must  be  cut  both  either  with  right  hand  threads 
or  with  left  hand  threads.  In  an  automobile  drive  with  the  en- 
gine rotating  right-handedly  as  usual,  worm  and  wheel  must  be 
cut  with  right  hand  threads  when  the  worm  is  placed  on  top  of 
the  wheel,  and  with  left  hand  threads  when  the  worm  is  at  the 
bottom. 

If  we  cut  a  very  thin  section  from  the  middle  of  the  worm 
wheel  we  have  a  spur  gear.  If  we  cut  a  corresponding  section 
from  the  worm,  we  have  a  rack,  and  since  the  flanks  of  a  rack 
tooth  to  properly  mesh  with  an  involute  gear  must  be  a  straight 
line,  the  faces  of  the  worm  teeth  are  straight.  In  the  old  type 
of  worm  used  for  transmitting  motion,  usually  at  a  very  high 
ratio  of  reduction,  the  sides  of  the  teeth  were  made  parallel,  and 
most  of  the  formulae  for  worm  gear  efficiency,  thrust,  etc.,  found 
in  text  books  are  based  on  square  faced  worm  teeth  and  are 
inaccurate  when  applied  to  inclined  teeth.  Parallel  faced  teeth 
cannot  be  used  on  multi-thread  worms  for  automobile  drives,  as 
the  worm  wheel  teeth  would  have  to  be  undercut  too  much. 

Pressure  Angle.  —  In  speaking  of  the  inclination  of  the  tooth 
flank,  a  distinction  must  be  made  between  the  normal  pressure 
angle  and  the  axial  pressure  angle.  The  axial  pressure  angle  is 
the  angle  made  by  the  line  of  intersection  of  a  plane  through  the 
worm  axis  with  the  tooth  flank,  with  the  worm  axis,  and  is  repre- 
sented by  j8  in  Fig.  190.  This  angle  is  evidently  one-half  of  the 
angle  described  by  the  tooth  flanks  in  the  section  plane  if  they  are 
continued  till  they  intersect.  The  normal  pressure  angle  a  is  the 
angle  included  by  two  lines  in  a  plane  cutting  the  tooth  normally 
or  at  right  angles  to  its  elements,  these  lines  both  passing  through 
the  pitch  point  in  the  tooth  flank,  one  being  perpendicular  to  the 
flank  at  that  point  and  the  other  tangent  to  the  pitch  circle.  The 
relation  between  the  axial  pressure  angle  and  the  normal  pressure 
angle  is  illustrated  in  Fig.  191.  In  this  figure  the  line  cd  is  sup- 
posed to  be  perpendicular  to  ac  and  not  in  the  plane  of  the  paper. 


296 


THE  WORM  DRIVE. 
be 


tan  /3  =  — 
ac 
cd 

tan  a  =  — 
ac 

cd  =  cb  cos  <t> 

Substituting  this  value  of  cd  in  the  preceding  equation  we  have 
cb  cos  0 

tan  a  = =  tan  ]8  cos  <t> 

ac 

That  is,  the  tangent  of  the  normal  pressure  angle  is  equal  to  the 
tangent  of  the  axial  pressure  angle  multiplied  by  the  cosine  of 
the  lead  angle. 


FlG.    190. — L  ONGITUD1NAL    SECTION 
THROUGH  WORM  WITH  30°  AXIAL  PRES- 
SURE ANGLE. 


FIG.  191.— RELATION 
BETWEEN  AXIAL 
PRESSURE  ANGLE  AND 
NORMAL  PRESSURE 
ANGLE. 


Most  makers  of  worm  gears  for  automobile  transmission  use 
an  axial  pressure  angle  of  30  degrees.  With  a  lead  angle  of  35 
degrees  this  corresponds  to  a  normal  pressure  angle  of  25  de- 
grees 19  minutes.  Normal  pressure  angles  of  22J^  and  14^  de- 
grees have  been  used,  but  with  these  smaller  pressure  angles  there 
is  undercutting  of  the  wheel  teeth  if  the  number  of  teeth  is  small. 
With  the  Hindley  type  of  worm  there  is  the  further  difficulty  that 
the  worm  could  not  be  assembled  with  the  wheel  if  the  pressure 
angle  were  too  small. 

Axial  Pitch. — In  ordinary  toothed  gearing,  as  the  tangential 


THE  WORM  DRIVE.  297 

pressure  which  can  safely  be  imposed  upon  the  gears  is  pro- 
portional to  the  circular  pitch  of  the  teeth,  the  coarseness  of  the 
teeth  increases  with  the  power  to  be  transmitted.  The  same 
relation  between  the  strength  of  the  teeth  and  their  circular 
pitch  exists  in  worm  gears,  but  as  the  load  capacity  depends 
more  upon  the  capacity  of  the  gears  for  getting  rid  of  the  fric- 
tional  heat  than  upon  the  mechanical  strength  of  their  teeth, 
and  as  the  heat  dispersing  capacity  of  a  gear  varies  little  with 
the  pitch  of  the  teeth,  the  latter  is  to  quite  an  extent  a  matter 
of  choice.  For  pleasure  cars  and  the  lightest  commercial  vehi- 
cles the  axial  pitch  is  generally  about  %  inch.  Axial  pitches  as 


FIG.  192.— COMPOSITION  OF  NORMAL  TOOTH  PRESSURE. 

4 

large  as  1^  inches  have  been  used  in  some  instances  in  heavy 
commercial  work,  but  pitches  of  about  1^4  inches  are  more  com- 
mon. The  larger  the  pitch  the  smaller  the  bottom  diameter  of 
the  worm,  and  even  if  the  worm  is  made  integral  with  the  shaft 
there  is  a  limit  to  the  depth  of  tooth,  and  consequently  to  the 
pitch,  because  if  the  proportion  of  the  depth  of  tooth  to  the  bot- 
tom diameter  of  the  worm  is  too  great  the  worm  will  possess 
insufficient  torsional  rigidity. 

The  length  of  the  worm,  if  of  the  straight  type,  is  usually  made 
2qual  to  40  per  cent,  of  the  wheel  pitch  diameter  and  the  included 
angle  of  worm  contact  may  vary  between  60  and  110  degrees,  but 
usually  is  closer  to  the  upper  limit.  The  lead  angles  usually  em- 
ployed vary  between  30  and  40  degrees.  This,  as  will  be  seen  from 
Fig.  194,  is  within  the  high  afficiency  range,  and  it  also  insures 
reversibility  of  the  drive,  that  is,  the  car  will  coast  freely  down 
hill  and  can  be  pushed  or  towed. 


298  THE  WORM  DRIVE. 

Theoretical  Efficiency. — When  power  is  being  transmitted 
from  the  worm  to  the  wheel,  there  are  two  forces  at  work, 
namely,  the  surface  pressure  normal  to  the  plane  of  contact  and 
the  frictional  force  in  the  plane  of  contact.  If  the  material  of  the 
worm  and  wheel  were  absolutely  unyielding  there  would  be  only 
a  line  contact,  but  since  it  is  elastic  the  contacting  parts  com- 
press so  as  to  give  a  surface  contact. 

Referring  to  Fig.  192,  the  normal  pressure  P  on  the  tooth  sur- 
face can  be  resolved  into  two  components,  one  P  cos  a,  perpen- 
dicular to  the  tooth  helix,  and  the  other,  P  sin  a,  parallel  thereto. 

The  former  component  is  transferred  to  Fig.  193  and  is  there 
again  resolved  into  two  components,  one,  P  cos  ct  sin  Q,  in  a 
plane  perpendicular  to  the  worm  axis  and  the  other  parallel  to 
the  worm  axis.  For  the  present  we  are  concerned  only  with  the 
former,  which  is  one  of  the  two  items  making  up  the  tangential 
force  at  the  pitch  line  of  the  worm.  The  other  item  is  due  to  the 
frictional  force  P  f  (f  being  the  coefficient  of  friction).  This 
force  can  also  be  resolved  into  two  components,  viz.,  P  f  cos  6 
tangential  to  the  worm  pitch  circle,  and  P  f  sin  6  tangential  to 
the  wheel  pitch  circle.  Hence  the  total  tangential  force  on  the 
worm  pitch  line  is 

P  cos  a  sin  9  +  P  f  cos  B 

and  the  total  tangential  force  on  the  pitch  line  of  the  wheel  is 
P  cos  a  cos  6  —  P  f  sin  6. 

Multiplying  these  tangential  forces  by  corresponding  motions 
on  the  pitch  circles  of  the  worm  and  the  wheel  respectively,  gives 
the  input  and  output  corresponding  to  that  motion,  respectively, 
and  the  ratio  of  the  latter  to  the  former  is  the  efficiency.  Sup- 
pose that  there  is  a  motion  x  in  the  direction  of  the  line  of  contact. 
Then  the  component  of  this  motion  tangential  to  the  worm  pitch 
line  is  x  cos  6  and  the  component  in  the  direction  of  the  wheel 
pitch  line,  x  sin  O.  Hence  the  ratio  of  velocities  is 

wheel  pitch  line  velocity         x  sin  0 

__ , =  =  tan  6 

worm  pitch  line  velocity          x  cos  © 

and  if  the  worm  moves  a  unit  distance  the  wheel  moves  a  dis- 
tance equal  to  tan  6.  Therefore,  the  work  done  upon  the  worm 
while  a  point  in  its  pitch  line  moves  a  unit  distance  is 

P  cos  o  sin  0  +  P  f  cos  6 
and  the  work  done  upon  the  wheel  is 

(P  cos  a  cos  0  —  P  f  sin  6)  tan  0. 
The  efficiency  then  is 


THE  WORM  DRIVE. 
(P  cos  a  cos  e  -^  p  f  sin  O)  tan  0 


299 


P  cos  «  sinO  +  P/cosO 

Dividing  both  numerator  and  denominator  by  P  cos  ©  tan  Q,  we 
have 

cos  a  —  /  tan  6 

«   -   -    (52) 

cos  a  +  /  cot  Q 


FIG.  193. — DIAGRAM  SHOWING  TANGENTIAL  FORCES  ON  WORM  AND 
WHEEL,  RESPECTIVELY,  AS  WELL  AS  THRUST  LOADS  ON  SHAFTS. 

which  is  the  general  formula  for  worm  wheel  efficiency.  Fig.  194 
shows  how  the  efficiency  varies  with  the  lead  angle  for  two  dif- 
ferent coefficients  of  friction,  viz.,  0.02  and  0.04. 


300 


THE  WORM  DRIVE. 


Thrust  and  Radial  Bearing  Loads. — The  thrust  load  on  the 
worm  is  equal  to  the  tangential  force  on  the  wheel  pitch  circle 
and  the  thrust  load  on  the  wheel  is  equal  to  the  tangential  force 
on  the  worm  pitch  circle.  The  effect  of  tooth  friction  can  be 
neglected,  as  in  well  cut  gears  with  proper  lubrication  the  friction 
coefficient  is  only  about  0.02,  and  the  error  introduced  by  neglect- 
ing it  is  very  slight.  Denoting  the  full  load  torque  of  the  engine 
by  T,  the  worm  pitch  diameter  by  d,  the  wheel  pitch  diameter  by 
D  and  the  reduction  ratio  by  r,  we  have  for  the  tangential  force 
on  the  worm  pitch  circle,  and  hence  for  the  thrust  load  on  the 
wheel,  at  full  engine  load  and  direct  drive. 


IUU 

x^ 

f-o.os 

^ 

^^~>~~ 

1 

ficieru 

/ 

^ 

^ 

\ 

\ 

^ 

f 

^ 

\l 

c 

\ 

\ 

/ 

9            £0            JO            40            SO            60             7O            QO            3C 

Angle  of  Lead  of  Worm,    in  Degrees 

FIG.  194. — EFFICIENCY  CURVES. 


24  T 


Lt  = 


(53) 


and  for  the  tangential  force  on  the  wheel  pitch  circle ;  and,  con- 
sequently, the  thrust  load  on  the  worm, 

24  Tr 

lt= ....       .       •       (54) 

D 

The  radial  loads  on  both  the  worm  and  the  wheel  shafts  are 
made  up  of  two  components  which  act  at  right  angles  to  each 
other.  The  first  is  due  to  the  pressure  angle  of. the  teeth;  it 
passes  through  the  center  of  tooth  contact  and  is  perpendicular 
to  both  the  worm  axis  and  the  wheel  axis.  This  is  the  force 
tending  to  separate  the  shafts  and  is,  of  course,  the  same  for 
both  the  worm  and  the  wheel.  If  we  denote  the  normal  tooth 


THE  WORM  DRIVE. 


301 


pressure  by  P,  then  this  component  Ci  is  equal  to  P  sin  a.     But 

It  Lt 

p  — — 


Hence 


cos  a  cos  <f>        cos  a  sin  <t> 


i  =  P  sin  a  = 


It  tan  a 


Lt  tan  a 


cos  <t>  sin  0 

The  other  component  of  the  radial  load,  C2,  is  different  for  the 
worm  and  the  wheel,  respectively.  For  the  wheel  it  is  equal  to 
the  thrust  load  on  the  worm,  It,  and  for  the  worm  it  is  equal  to 
the  thrust  load  on  the  wheel,  Lt.  That  the  two  components  of 
the  radial  load  on  each  shaft  are  at  right  angles  to  each  other 
may  easily  be  shown.  Take,  for  instance,  the  components  of  the 
radial  load  on  the  wheel  shaft.  The  first  component,  Ci  is  per- 
pendicular to  the  worm  shaft,  while  the  second  component,  the 
thrust  load  on  the  worm  shaft,  naturally  is  parallel  to  that  shaft 
and  hence  must  be  perpendicular  to  the  first  component.  There- 


FIG.  195.— WORM  WITH  FIVE  THREADS,  33  DEGREES  LEAD 
ANGLE,  30  DEGREES  PRESSURE  ANGLE. 

fore,  the  total  radial  load  on  the  wheel  shaft  is  equal  to  the  square 
root  of  the  sum  of  the  squares  of  the  components 


T        

Zw  r 


tan  a 

But =  tan  |8, 

cos  <t> 

so  that 


Lr  =  /t\i  +  tan"2  |3        .....       .       (55) 

and  if  /3,  the  axial  pressure  angle,  has  a  constant  value  of  30  de- 
grees then 

Lr  =  1.155ft 

That  is,  the  radial  load  on  the  wheel  bearings  is  15.5  per  cent, 
greater  than  the  thrust  load  on  the  worm  bearings. 


302  THE  WORM  DRIVE. 

Similarly,  the  total  radial  load  on  the  worm  shaft  is 


tan  a  tan  a     * 


sin  <  sin 

which,  after  the  value  of  tan  a  is  substituted,  becomes 


/  tan  ft  \ * 

+ .       .      .  .-  ,      (56) 

\tan  <t>  / 

Center  Distance. — The  distance  between  the  axis  of  the  worm 
and  the  axis  of  the  wheel  bears  a  close  relation  to  the  maximum 
torque  to  be  transmitted  and  therefore  to  the  total  weight  of  the 
vehicle.  In  commercial  vehicle  practice  the  smallest  distance 
between  axes,  or  the  center-to-center  distance,  found  in  %  ton 
and  1  ton  trucks,  is  about  6^4  inches.  For  5  ton  trucks  a  center- 
to-oenter  distance  of  about  9}/2  inches  is  used,  and  for  worm  gears 
for  motor  trucks  of  other  capacities  the  center  distance  may  be 
found  approximately  by  the  following  equation 

L  =  0.7  t  +  6  inches  .       .       .       .       (57) 

where  t  is  the  truck  capacity  in  tons. 
As  the  worm  pitch  diameter 

n  p 


IT  tan  <t> 
and  the  wheel  pitch  diameter 

AT* 


D  = 

7T 

and  as  the  center  distance 

d 

L  = 

we  have 


(58) 

Capacity  of  Worm  Gears. — The  question  of  the  amount  of 
power  which  a  given  worm  will  transmit  is  a  very  involved 
one.  It  depends  more  upon  the  capacity  of  the  gear  for  dis- 
posing of  the  heat  than  upon  the  mechanical  strength  of  its 
teeth.  As  the  temperature  of  the  worm  and  wheel  and  of  the 


THE  WORM  DRIVE.  303 

oil  bath  rises,  the  oil  becomes  thinner,  and  if  it  should  become 
too  thin  it  would  be  squeezed  out  from  between  the  teeth  and 
cutting  would  ensue.  The  heat  produced  is  almost  directly 
proportional  to  the  horse  power  transmitted.  On  the  other  hand, 
the  amount  of  heat  which  the  gear  can  dispose  of  without  an 
excessive  rise  in  temperature  is  proportional  to  the  combined 
surface  area  of  the  worm  and  wheel.  Of  this  the  surface  area 


FIG.  196.— THIRTY-EIGHT  TOOTH  WORM  WHEEL,  WITH  33  DEGREES 
ANGLE  OF  LEAD  AND  30  DEGREES  PRESSURE  ANGLE. 

of  the  wheel  is  by  far  the  greater  part.  The  total  surface  area 
of  the  gear  is  substantially  proportional  to  the  aggregate  area 
of  the  sides  or  flanks  of  its  teeth,  which  varies  directly  as  the 
wheel  pitch  diameter,  the  worm  pitch  diameter  and  the  sub- 
tended angle  of  the  wheel  teeth.  There  is  no  doubt  that  the 


304  THE  WORM  DRIVE. 

capacity  of  a  worm  and  gear  combination  increases  with  the 
subtended  angle  of  the  wheel  teeth,  for  by  successively  reducing 
the  subtended  angle  of  any  successful  worm  gear  a  point  would 
soon  be  reached  where  the  gear  would  fail  under  its  load.  How- 
ever, as  an  increase  in  the  subtended  angle  increases  only  the 
wheel  area  and  that  not  in  direct  proportion,  whereas  the  worm 
area  fs  not  increased  at  all,  it  is  not  to  be  expected  that  the 
capacity  will  increase  directly  as  the  subtended  angle.  It  will 
not  be  wide  off  the  mark  if  we  assume  that  it  increases  as  the 
square  root  of  the  subtended  angle. 

There  is  another  aspect  to  the  problem.  With  a  given  worm 
gear  we  could  transmit  a  certain  horse  power  either  at  high 
rubbing  speed  and  low  tooth  pressure  or  at  low  rubbing  speed 
and  high  tooth  pressure.  Within  reasonable  limits  of  speed 
and  tooth  pressure  there  would  not  be  much  variation  in  heat 
production.  However,  with  the  lower  tooth  pressure  the  tem- 
perature could  be  carried  higher  without  danger  of  the  oil  film 
being  broken  down.  This  alone  would  result  in  an  increase  in 
capacity,  and  a  further  increase  would  result  from  the  fact  that 
at  this  higher  temperature  the  gear  would  disperse  more  heat. 
Therefore,  in  giving  a  constant  for  capacity  it  will  be  well  to 
limit  its  application  to  a  small  range  of  rubbing  speeds.  The 
writer  finds  that  worm  gearing  for  motor  trucks  where  the 
rubbing  speed  is  between  1,000  and  1,200  feet  per  minute  is 
given  by 

H.P.  =  0.1  d  D  \]^~ 

where  d  is  the  worm  pitch  diameter,  D  the  wheel  pitch  dia- 
meter and  <£  the  angle  (in  degrees)  subtended  by  the  wheel 
teeth. 

Another  rule  for  the  capacity  of  worm  gears,  due  to  F.  W. 
Lanchester,  is  one  long  ton  per  square  inch  of  projected  worm 
tooth  area.  Mr.  Lanchester  says  that  his  worm  gear  will  trans- 
mit a  load  corresponding  to  such  a  pressure  for  an  indefinite 
period.  Now,  a  worm  gear  for  automobile  transmission  must 
evidently  have  a  transmitting  capacity  enabling  it  to  support 
pressures  considerably  greater  than  that  corresponding  to  full 
engine  power  on  the  direct  drive  for  sometimes  the  full  engine 
power  will  be  developed  on  the  low  gear  or  the  reverse.  This 
latter  condition,  however,  generally  does  not  last  for  any  length 
of  time,  hence  it  is  not  necessary  that  the  gear  should  be  cap- 
able of  supporting  the  full  engine  power  transmitted  through 
the  low  gear  indefinitely.  In  truck  transmissions  the  usual  al- 


THE  WORM  DRIVE. 


305 


lowance  is  1,200-1,400  Ibs.  per  square  inch  of  projected  tooth 
area  in  contact,  based  on  full  engine  power  on  the  direct  drive. 
If  d  be  the  pitch  diameter  of  the  worm,  the  outside  diameter  is 
d  +  2p*/K  and  the  bottom  working  diameter  d  —  2/>a/7r;  and  if 
the  angle  of  worm  contact  be  0,  then  the  projected  area  of  worm 
contact  is 


FIG.  197,— SHADOW  VIEW  OF  WORM  WHEEL  AXLE. 


/  2    />a\2         /  2 

d  +  I—id 1  X  —  X =  square 

V  *•   /      \  T   /        4         360  180 

inches. 

Efficiency   Tests   of    Worm    Gears. — Several    series    of   effi- 
ciency tests  have  been  carried  out  on  worm  gears   for  autorno- 


306 


THE  WORM  DRIVE. 


bile  drives.  One  of  the  earliest  extensive  tests  reported  was 
made  by  the  H.  H.  Franklin  Mfg.  Co.,  and  showed  efficiencies 
of  88-89  per  cent,  at  worm  speeds  of  1,200  and  1,500  r.p.m.  over 
an  output  range  from  8  to  20  h.p.  This  is  a  rather  low  effi- 
ciency, but  it  must  be  remembered  that  these  tests  were  made 
at  a  rather  early  period  and  the  fact  that  the  Franklin  Com- 
pany discontinued  the  worm  drive  would  seem  to  warrant  the 
assumption  that,  the  gears  were  not  particularly  good  examples 
of  the  art  of  worm  gear  cutting. 


FIG.  198. — LANCHESTER  WORM  GEAR  TESTING  MACHINE. 

In  1912  several  series  of  tests  of  Lanchester  worm  gears 
were  made  by  the  National  Physical  Laboratory  of  England 
for  the  Daimler  Motor  Company  on  a  special  testing  machine 
designed  by  Mr.  Lanchester.  This  machine  is  based  on  a  prin- 
ciple similar  to  that  of  the  electric  cradle  dynamometer.  It 
has  been  repeatedly  pointed  out  that  the  rear  axle  housing 
tends  to  turn  in  the  direction  opposite  to  that  of  the  axle  shafts, 
with  a  torque  exactly  equal  to  that  of  the  axle  shafts.  There- 
fore, by  mounting  the  rear  axle  housing  in  ball  bearing  sup- 
ports and  holding  it  from  rotation  by  means  of  a  weight  on  an 


THE  WORM  DRIVE.  307 

arm  secured  to  the  housing,  we  have  a  measure  of  the  rear  axle 
torque.  If  the  axle  is  worm  driven,  the  housing  also  has  a 
tendency  to  turn  in  a  plane  perpendicular  to  the  worm  axis  in 
the  direction  opposite  to  that  of  the  worm  shaft,  with  a  torque 
equal  to  that  of  the  worm  shaft.  Lanchester,  therefore,  gives 
his  worm  gear  housing  such  a  support  that  it  may  rock  in  two 
vertical  planes  at  right  angles  to  each  other.  He  then  measures 
the  torque  on  the  propeller  shaft  and  on  the  axle  shaft,  respec- 
tively, by  balancing  the  housing  in  both  planes.  This  he  does 
by  means  of  a  single  weight  suspended  from  a  knife  edge  paral- 
lel with  and  at  a  given  distance  from  the  axle  shaft  axis. 

If  we  denote  the  torque  on  the  worm  shaft  by  t,  that  on  the 
axle  shafts  by  T  and  the  worm  gear  reduction  ratio  by  r,  then 
if  there  were  no  loss  in  the  gear  we  would  have 


As  a  matter  of  fact  T  is  always  less  than  t  r,  and  the  efficiency 
is  measured  by  the  ratio  Tit  r. 

The  testing  machine  comprises  a  cradle  consisting  of  two 
wheels  coupled  by  bridges.  The  cradle  is  supported  by  four 
ball-bearing  rollers  and  power  is  transmitted  to  the  worm  and 
from  the  rear  hub  universal  jointed  shafts,  the  joints  being  of 
the  ball  bearing  type.  A  balance  arm  is  fixed  to  one  side  of  the 
case  parallel  to  the  worm  shaft.  At  the  end  of  this  arm  there  is 
a  transverse  knife  edge  arm  on  which  a  weight  is  suspended  by 
means  of  a  rod.  The  weight  can  be  slid  along  the  transverse 
arm  by  means  of  a  finger  wheel,  and  its  distance  from  the  axis 
of  suspension  can  be  read  off  on  a  dial. 

The  gear  box  is  supported  from  the  cradle  on  ball  bearings 
in  such  a  way  that  the  axis  of  the  worm  intersects  the  axis  of 
the  cradle  wheels.  When  the  worm  gear  housing  is  in  equi- 
librium the  contact  point  of  the  knife  edge  is  located  in  the 
plane  of  the  two  axes  of  rotation.  In  operation  the  finger  wheel 
is  adjusted  until  the  gear  box  is  in  equilibrium.  Then,  as  the 
same  weight  is  used  to  measure  the  torque  around  each  axis  of 
support,  the  torques  are  proportional  to  the  distances  of  the  point 
of  knife  edge  contact  from  the  two  axes  of  support,  respectively. 
We  found  that 

T          T         1 

t  r          t         r' 
and  since 

T        OA 

_  =  --  (see  Fig.  199) 

t        AB 


308 


THE  WORM  DRIVE. 


OA         1 

e  = X  — 

AB         r 

In  order  to  be  able  to  make  efficiency  tests  of  large  worm 
gears  with  a  small  expenditure  of  energy,  Lanchester  connects 
his  driven  shaft  (or  axle  shaft),  through  a  step-up  bevel  gear 
set  and  a  belt  to  the  worm  shaft,  the  step-up  ratio  being  slightly 
greater  than  the  reduction  of  the  worm  and  worm  wheel,  so  that 
the  belt  always  slips  slightly.  As  a  result  only  the  power  lost 
in  the  worm  gear,  bevel  gear  and  in  belt  slip  needs  to  be  sup- 
plied from  an  outside  source.  The  belt  tension  is  adjusted  until 
the  weight  hung  from  the  knife  edge  is  lifted  and  when  mid- 
way between  stops  the  arm  is  locked  in  position.  Readings  are 
then  taken,  and  afterwards  the  arm  is  released  to  see  whether 
the  torque  has  changed.  Slight  changes  in  torque  do  not  affect 
the  efficiency,  consequently  it  is  not  necessary  to  constantly 
adjust  the  weight. 


FIG.  199. — DIAGRAM  OF  TORQUE  BALANCE. 


The  chief  results  of  the  National  Physical  Laboratory  tests 
on  Lanchester  worm  gears  are  summarized  in  the  following 
tables,  only  the  readings  and  calculated  results  for  the  highest 
and  the  lowest  speed  in  each  series  being  given : 


Worm 
Speed 
R.P.M. 
1542 

383 
1532 

408 
1532 

403 
1532 

373 
1497 

418 


8 

:33  WORM  GEAR 

Torque 
on  Driven 

Calculated 

Efficiency 

Shaft 

H.P. 

P.C. 

Lbs.-Ft. 

31.9 

95.4 

449 

7.9 

93.9 

449 

45.6 

95.7 

645 

12.1 

94.0 

645 

59.4 

95.8 

841 

15.6 

93.8 

841 

73.3 

95.7 

1035 

17.8 

93.7 

1037 

17.5 

93.5 

254 

4.9 

93.6 

254 

Pressure 

on 

Thread 
Lbs. 
1205 
1205 
1733 
1733 
2258 
2258 
2786 
2786 
682 
682 


THE  WORM  DRIVE.  309 

8:35  WORM  GEAR 

1532        29.8        95.7         447        1200 

418         8.1        94.6         447        1200 

1512        42.3        96.2         643        1727 

413        11.6        95.1         643        1727 

1532        69.0        95.6        1035        2780 

398  17.9  93.1  1035  2780 

9:34  WORM  GEAR 

1532  34.5  96.0  447  1200 

393  8.9  95.2  447  1200 

1527  49.5  96.6  613  1727 

403  13.1  95.0  613  1727 

1527  79.6  96.6  1035  2780 

403  21.0  95.0  1035  2780 

Application  of  Formulae — We  may  now  illustrate  the  appli- 
cation of  the  formulae  developed  in  the  foregoing  by  the  example 
of  a  worm  gear  drive  for  a  three  ton  truck.  Let  the  truck  be 
equipped  with  a  four  cylinder  ^l/2  x  5  inch  motor  (torque  =  165 
lbs.-ft). 
According  to  equation  (57)  the  center  distance  must  be  about 

6+  (3  X  0.7)  =  8.1  inches. 

The  usual  gear  reduction  for  this  size  of  truck  is  about  9  to  1, 
hence  we  may  choose  4  and  36  teeth,  at  least  for  a  trial.  We  then 
have  (equation  58) 


+  36  )=8.1  inches 
6.2832  \tan  <j> 
4p 

-  +  36  p  =  50.894 
tan  <j> 
If  we  choose  a  lead  angle  of  30  degrees  then 

+  36  p  =  50.894 

0.577 

42.94  p  =  50.894 
p  =  1.185  inches. 
The  worm  pitch  diameter  will  be 
4  X   1.185 

— =  2.614  inches. 

3.1416  X  0.577 
The  lead  of  the  worm  will  be 

2.614  X  3.1416  X  0.577  =  4.738  inches. 
The  pitch  diameter  of  the  wheel  will  be 
36  X   1.185 

=  13.579  inches 

3.1416 
and  the  lead  of  the  wheel 

13.579  X  3.1416 

-  =  73.932  inches. 
0.577 


310  THE  WORM  DRIVE. 

The  outside  diameter  of  the  worm  will  be 
2  X   1.185 

2.614  +  • =  3.368 

3.1416 
The  outside  diameter  of  the  wheel  will  be 

2  X  1.185 
13.579  +  =  14.333 

3.1416 

The  thrust  load  on  the  worm  shaft  will  be 
24  X   165  X  9 

=  2625  Ibs. 

13.579 

The  thrust  load  on  the  wheel 
24  X   165 

=  1514  Ibs. 

2.614 

The  radial  load  on  the  wheel  shaft 

1.155  X  2625  =  3030  Ibs. 
and  the  radial  load  on  the  worm  shaft 


1    i-  2140- Ibs. 


/  0.577 

\  0.577 

The  one  thing  which  remains  to  be  determined  is  the  included 
angle  of  the  wheel  rim.  Suppose  that  the  4.^2  x  5  inch  four 
cylinder  motor  runs  at  1200  r.p.m.  and  develops  a  brake  mean 
effective  pressure  of  70  pounds  per  square  inch.  Then  its  horse- 
power is  33.8.  Therefore  (equation  page  304). 

33.8  =  0.1  X  2.614  X  13.579 


=  9.5 

0  =  90  degrees. 

Materials. — The  worm  is  made  of  low  carbon  steel  and  is  case 
hardened.  The  wheel  is  made  of  hard  phosphor  bronze.  These 
materials  are  used  because,  owing  to  their  hardness,  they  will 
withstand  great  surface  pressure,  and  also  because  they  may  be 
finished  to  a  high  polish.  The  phosphor  bronze  wheel  blank 
should  be  cast  with  plenty  of  finishing  stock,  so  that  all  porous 
metal  may  be  removed  in  the  machining.  The  worm  and  wheel 
are  generally  cut  by  means  of  hobs.  In  cutting  the  teeth  the 
greatest  accuracy  must  be  aimed  at  and  the  surfaces  must  be 
smoothly  finished,  so  that  there  is  no  need  for  much  polishing 
after  hardening. 

Hardening  and  Polishing  of  Worms. — The  following  rules 
regarding  the  carbonizing,  quenching  and  polishing  of  worms 


THE  WORM  DRIVE.  311 

were  given  by  T.  Rapson  in  an  article  in  The  Automobile  Engi- 
neer (London)  for  May,  1912: 

"If  the  worm  shafts  are  packed  carefully  in  a  carbonizing 
medium,  such  as  bone-dust,  charcoal,  etc.,  the  box  is  properly 
'clayed  up,'  placed  in  a  carbonizing  furnace  and  kept  at  the 
proper  temperature,  is  then  removed  and  the  worms  are  left 
to  cool  in  the  box,  there  will  be  little  trouble  from  oxidation. 
They  should  be  removed  from  the  boxes,  thoroughly  brushed 


FIG.  200. — HOBBING  A  WORM  WHEEL. 

(In  the  shops  of  Henry  Wallwork  &  Co.,  Ltd.,  Manchester,  England.) 

and  cleaned  (not  with  a  stiff  wire  brush),  then  immersed  in  a 
bath  of  diluted  hydrochloric  and  nitric  acid  for  about  five 
minutes,  removed  and  washed  in  a  soda  bath,  dried  in  sawdust, 
and  are  then  ready  for  hardening.  During  the  carbonizing  opera- 
tion all  screw  threads  (if  any),  and  the  centres  on  which  the 
worm  shafts  will  run  when  being  ground  for  the  ball  races,  should 
be  covered  with  a  solution  of  copper  sulphate,  about  four  or  five 
ounces  to  a  pint  of  water.  This  will  keep  the  places  so  covered 


312  THE  WORM  DRIVE. 

from  being  carbonized  and  allow  the  centres  to  be  scraped,  if 
necessary,  after  the  hardening  process,  to  ensure  the  worm  run- 
ning true  before  grinding  for  the  bearings  or  races. 

"To  prevent  scaling  the  worms  during  the  hardening  opera- 
tion, a  salt  heating  bath  should  be  used,  i.  e.,  the  worms  should 
be  heated  in  melted  salt,  which  will  allow  them  to  be  brought 
to  a  temperature  suitable  for  hardening  without  allowing  them 
to  come  in  contact  with  oxidizing  influences;  also  the  salt  forms 
a  coating  when  the  worms  are  being  transferred  from  the  bath 
to  the  quenching  vat.  The  reader  may  readily  try  this  method 
by  obtaining  a  large,  gannister  lined  plumbago  crucible,  putting 
in  a  quantity  of  barium  chloride,  and  heating  to  from  700  to  750 
degrees  C.  (roughly,  about  the  temperature  at  which  aluminum 
melts),  placing  a  worm  in  the  melted  salt  and  allowing  it  to 
get  to  the  surrounding  temperature,  which  will  take  from  seven 
to  ten  minutes.  It  must  then  be  removed  and  plunged  into  a 
bath  of  cold  water.  After  the  worm  is  cold  it  can  be  dipped 
in  a  hydrochloric  acid  bath,  which  will  free  the  barium  chloride, 
allowing  it  to  be  washed  away  readily,  and  a  soda  bath,  with  a 
good  drying  in  sawdust  will  leave  a  surface  just  as  though  it 
had  not  been  heated. 

The  worm  is  now  ready  for  polishing  and,  if  the  beforemen- 
tioned  precautions  have  been  taken  in  machining,  carbonizing 
and  hardening,  this  will  be  a  comparatively  easy  matter.  A  most 
satisfactory  polish  may  be  attained  by  mounting  an  endless  belt, 
one  side  of  which  has  a  section  equal  to  the  space  between  the 
worm  teeth,  set  at  the  angle  of  the  lead  of  the  worm,  the  worm 
being  mounted  on  dividing  heads  and  a  reciprocating  table  which 
permits  its  lateral  and  rotary  movement,  while  the  position  of 
the  belt  is  constant.  The  belt  must  be  kept  tight  by  a  weight  or 
spring  and  its  section  be  corrected  for  interference,  as  in  the  case 
of  the  cutter  for  the  thread  milling  machine,  but  in  this  case  for 
an  infinite  diameter  or  straight  line.  It  should  run  at  a  surface 
speed  of  from  6,000  to  7,000  feet  per  minute,  and  be  coated  with 
very  fine  abrasive.  For  the  finishing  operation  the  belt  should 
be  replaced  by  a  soft  cotton  rope  and  fed  with  crocus  and  oil." 

Hindley  Worm  Gear. — All  worm  wheels  are  "throated" — that 
is,  the  face  of  the  gears,  instead  of  being  turned  off  straight,  is 
turned  to  an  arc  of  a  circle  of  a  radius  slightly  greater  than  the 
outside  radius  of  the  worm.  The  object,  of  course,  is  to  increase 
the  tooth  contact  area.  It  is  also  possible  to  "throat"  the  worm, 
and  this  form  of  worm  is  known  as  the  Hindley.  Such  a  worm 
insures  increased  bearing  surface,  and  therefore  is  less  liable  to 


THE  WORM  DRIVE. 


313 


start  cutting.  However,  its  machining  involves  some  difficulty 
and  it  requires  additional  care  in  mounting.  The  ordinary  straight 
worm  must  be  mounted  accurately  in  two  planes;  that  is,  the 
worm  axis  must  be  at  a  definite  distance  from  the  wheel  axis,  and 
it  must  also  be  in  the  median  plane  of  the  worm  wheel.  The 
Hindley  or  "hour  glass"  worm,  on  the  other  hand,  must  be  ac- 
curately located  in  three  planes;  that  is,  the  worm  axis  must 
be  a  definite  distance  from  the  wheel  axis;  it  must  be  in  the 
median  plane  of  the  worm  wheel,  and  the  median  plane  of  the 
worm  must  include  the  wheel  axis.  In  cutting  a  Hindley  worm 
the  cutting  tool  must  be  mounted  so  as  to  turn  around  a  centre 
at  a  distance  from  the  cutting  edge  equal  to  the  radius  of  the 
worm  wheel,  and  it  must  be  fed  in  the  direction  perpendicular 
to  the  plane  of  rotation  of  the  worm. 


FIG.  201.— HINDLEY  TYPE  WORM. 

(Purposely  shown  longer  than  made  in  practice,  to   bring  out  "hour  glass" 
effect   more   clearly.) 

The  majority  of  worm  drives  in  England  seem  to  employ 
straight  worms,  but  the  Lanchester  worm,  which  is  used  on 
several  foreign  makes  of  cars  and  is  being  introduced  in  this 
country,  is  of  the  Hindley  type.  When  proper  manufacturing 
equipment  is  available  the  manufacturing  difficulties  vanish,  and 
there  remains  only  the  greater  difficulty  involved  in  properly 
mounting  the  Hindley  worm  to  balance  the  advantage  of  a  lower 
unit  tooth  pressure.  The  Hindley  worm  is  made  shorter  than  the 
straight  worm,  usually  between  one-fifth  and  one-quarter  the 
wheel  diameter. 


314 


THE  WORM  DRIVE. 


Location  of  Worm  Relative  to  Wheel. — As  already  pointed 
out,  there  are  two  possible  arrangements  of  the  worm  and  wheel 
combination,  viz.,  with  the  worm  at  the  bottom  and  at  the  top 
of  the  wheel  respectively.  As  far  as  the  operation  of  the  worm 
gear  is  concerned,  the  former  is  the  preferable  arrangement,  be- 
cause with  it  the  worm  is  always  submerged  in  oil,  as  is  that 
portion  of  the  wheel  whose  teeth  are  at  the  moment  meshing  with 
those  of  the  worm.  The  heat  developed  by  the  friction  at  the 
tooth  contact  has  to  be  transmitted  to  the  casing  largely  through 
the  oil  bath,  and  when  the  worm  is  at  the  bottom  the  path 


FIG.  202.— MOUNTING  OF  WORM  WITH  ONE  PLAIN  AND  ONE  BALL 
THRUST  BEARING. 


FIG.   203.— MOUNTING   OF   WORM   WITH    DOUBLE   BALL   THRUST 

BEARINGS. 

for  the  heat  to  travel  is  shorter  and  more  direct.  However,  in 
American  practice  considerations  of  ground  clearance  required 
practically  exclude  the  bottom  mounted  worm,  except  on  town 
cars.  Practical  experience,  moreover,  has  shown  that  it  is  per- 
fectly possible  to  properly  lubricate  the  top-mounted  worm  and 


THE  WORM  DRIVE. 


315 


to  keep  it  cool,  as  at  moderate  and  high  speeds  the  revolving  wheel 
throws  oil  over  the  whole  interior  of  the  driving  gear  housing. 

Mounting  of  Worm. — A  very  heavy  thrust  comes  on  the 
worm  shaft  when  the  full  engine  load  is  being  transmitted,  and 
special  thrust  bearings  must  be  provided.  With  a  top-mounted 
worm  the  thrust  is  toward  the  rear  when  the  car  is  being  driven 
forward  and  toward  the  front  when  it  is  being  driven  backward. 
Since  the  thrust  load  is  greater  than  the  radial  load,  and  must 
be  carried  by  a  single  bearing,  whereas  the  radial  load  is  divided 
between  two  bearings,  it  is  customary  to  use  separate  thrust 


FIG.  204. — MOUNTING  OF  WORM  DRIVEN  DIFFERENTIAL. 

bearings.  The  reverse  is  used  only  rarely,  and  then  generally 
only  under  low  power  and  for  a  short  time;  hence,  a  pair  of 
plain  thrust  washers  are  sometimes  used  for  it,  as  shown  in 
Fig.  202,  with  a  ball  thrust  bearing  to  take  up  the  thrust  due 
to  forward  driving.  However,  the  more  common  plan  is  to  use 
a  double  ball  thrust  bearing,  as  illustrated  in  Fig.  203.  The 


316  THE  WORM  DRIVE. 

differential  also  has  to  be  provided  with  thrust  bearings  for  taking 
thrust  in  both  directions,  and  in  this  case  either  a  single  ball 
thrust  bearing  may  be  mounted  on  either  side  of  the  differential 
or  a  double  thrust  bearing  on  one  side.  The  usual  plan  is  to 
place  one  thrust  bearing  on  either  side  of  the  differential,  which 
is  illustrated  in  Fig.  204.  As  regards  the  sizes  of  bearings, 
the  same  rule  can  be  followed  as  given  for  the  differential 
bearings  of  bevel  driven  rear  axles,  viz.,  to  use  bearings  of  50  to 
100  per  cent,  greater  rated  load  capacity  than  the  maximum  load 
they  will  have  to  carry  with  the  direct  drive  in  operation.  Of 
all  the  bearings  of  a  worm  drive  shaft  the  worm  shaft  thrust 
bearing  has  to  carry  the  largest  load,  and  it,  therefore,  should 
be  made  of  liberal  size. 

Driving  Gear  Housings. — The  driving  gear  housing  of  a  worm 
driven  axle  may  be  divided  in  three  planes,  viz.,  vertically  in  a 
fore  and  aft  plane,  vertically  in  a  transverse  plane  and  horizontal- 
ly. It  may  also  be  made  in  a  single  casting.  In  the  Fierce-Arrow 
motor  truck  the  housing  is  cast  in  a  single  piece,  with  a  large 
gear  carrier  fitted  to  the  top,  as  illustrated  in  Fig.  205.  In  the 
case  of  a  bottom  mounted  worm,  the  casing  may  be  cast  in  a 
single  piece  with  a  large  cover  on  top  or  at  an  angle  of  45  de- 
grees, through  the  opening  of  which  the  differential  may  be  in- 
serted. The  worm  is  always  located  in  a  tunnel  which  is  bored 
out  for  the  reception  of  the  bearings,  and  generally  the  bear- 
ings at  one  end,  at  least,  are  larger  in  diameter  than  the  worm, 
so  that  the  whole  worm  shaft  assembly  can  be  inserted  into  the 
tunnel  from  that  end.  In  some  designs,  however,  the  casing  is 
split  through  the  worm  axis. 

Undoubtedly  the  greatest  rigidity  with  a  given  amount  of 
material  is  obtained  by  dividing  the  housing  vertically  per- 
pendicularly to  the  axis  of  the  differential,  but,  unfortunately, 
this  design  is  not  very  satisfactory  from  the  standpoint  of  con- 
venience in  assembling.  The  gear  carrier  principle,  when  applied 
to  the  worm  driven  axle  possesses  all  of  the  advantages  that 
it  does  in  connection  with  the  bevel  driven  axle,  accurate  meshing 
of  teeth  being  fully  as  important  with  the  worm  gear  as  with 
the  bevel  gear.  In  the  United  States  practically  all  worm  driven 
axles  are  designed  on  the  gear  carrier  principle,  which  has  proven 
absolutely  satisfactory. 

The  torque  reaction  is  exactly  the  same  in  a  worm  driven  axle 
as  in  a  bevel  gear  driven  axle,  and  must  be  taken  up  by  the  same 
means.  Also,  the  action  of  the  body  springs  has  exactly  the 
same  effect  on  the  worm  drive  as  on  the  bevel  gear  drive,  and 


THE  WORM  DRIVE. 


317 


the  relative  merits  of  the  different  axle  linkages  are  the  same 
for  the  worm  drive  as  for  the  bevel  gear  drive.  It,  therefore,  is 
unnecessary  to  go  into  the  design  of  these  parts  in  connection 
with  the  worm  drive.  The  design  of  the  axle  housing  with 
respect  to  strength  also  is  the  same  as  for  a  bevel  gear  driven 
axle,  except  that  the  worm  drive  is  often  used  for  commercial 
vehicles  of  relatively  low  speed  in  which  the  limiting  stress  on 


FIG.  205.— DRIVING  GEAR  HOUSING  WITH  GEAR  CARRIER  (FIERCE- 
ARROW  TRUCK). 

the  axle  housing  is  less.  A  live  axle  to  carry  a  weight  of  several 
tons  and  to  withstand  the  reactions  due  to  the  forces  necessary 
to  propel  such  a  load  must  of  necessity  be  of  great  strength. 
Until  1915  the  majority  of  truck  axles  were  dead  axles,  and  there 
was  some  bias  against  live  axles  for  heavy  vehicles  among  de- 
signers. There  seems  to  be  no  reason,  however,  why  a  live  axle 
cannot  be  made  strong  enough  to  carry  any  load  that  can  pos- 


318  THE  WORM  DRIVE. 

sibly  be  put  onto  a  truck.  However,  every  effort  must  be  made 
to  so  arrange  the  design  that  the  moments  and  couples  are  re- 
duced to  a  minimum  and  to  so  distribute  the  metal  that  it  works 
to  the  best  advantage. 

Calculation  of  Axle  Tube  Dimensions. — We  saw,  in  con- 
nection with  bevel  driven  live  axles,  that  the  axle  housing  is 
subjected  to  three  different  stresses,  as  follows:  (1)  The  ver- 
tical bending  stress  due  to  the  weight  carried;  (2)  the  hori- 
zontal bending  stress  due  to  the  driving  thrust  of  the  wheels 
or  the  retarding  force  of  the  wheels  in  braking,  and  (3)  the 
torsional  stress  on  the  axle  tubes  due  to  the  application  of  the 
rear  wheel  brakes.  Of  these  the  first  can  be  greatly  reduced  by 
means  of  an  underrunning  truss,  and  the  second  can  be  reduced 
and  the  third  practically  eliminated  by  using  separate  torque 
arms  for  the  driving  and  braking  torque,  respectively.  Two 
torque  arms  should  be  used  for  the  braking  torque,  each  close  to 
one  of  the  brakes,  and  either  integral  with  the  brake  supporting 
bracket  or  pivotally  secured  to  it.  The  forward  ends  £>f  these 
torque  arms  should  be  secured  to  the  frame  in  such  a  manner 
that  they  will  transmit  the  forward  driving  thrust  to  the  frame. 
The  lever  arm  of  the  bending  moment  due  to  the  driving  thrust 
or  braking  pull  is  then  much  shorter,  being  equal  to  the  distance 
between  the  centre  plane  of  the  driving  wheel  and  the  radius 
rod,  instead  of  to  the  distance  between  the  wheel  and  the  point 
where  the  axle  tube  enters  the  driving  gear  housing.  Besides, 
since  the  torque  bar  is  directly  connected  to  the  brake  support, 
the  reaction  on  the  brake  support  is  transmitted  directly  to  it 
and  does  not  create  any  torsion  in  the  axle  tube.  There  are  then 
only  bending  stresses  on  the  axle  tube,  due  to  the  horizontal  and 
vertical  moments,  respectively. 

Suppose  that  in  a  3  ton  truck  the  load  on  each  rear  wheel 
when  the  truck  is  fully  loaded  is  4,000  pounds.  Also  that  the 
distance  from  the  centre  plane  of  the  rear  wheel  to  the  centre 
of  the  body  spring  is  13  inches  and  the  distance  from  the  centre 
plane  of  the  wheel  to  the  centre  of  the  radius  rod  7  inches.  With 
a  coefficient  of  slippage  of  0.6  the  maximum  driving  force  which 
can  be  exerted  at  the  wheel  rims  is  2,400  pounds.  Hence  the 
maximum  bending  moment  on  the  axle  housing  is 

^(4,000  X  13)2  +  (2,400  X  7)2  =  54,600  pounds-inches. 


THE  WORM  DRIVE.  319 

Since  the  moment  due  to  the  weight  supported  alone  is 
52,000  pounds-inches  it  is  seen  that  the  additional  moment 
due  to  the  wheel  thrust  is  negligible  when,  as  in  this  case,  the 
radius  rods  are  located  close  to  the  rear  wheels.  In  regular 
operation  a  considerable  portion  of  the  stress  on  the  axle  hous- 
ing is  taken  up  on  the  axle  truss  rod.  We  will  assume  that  the 
axle  tube  is  to  be  funnel-shaped  with  flanged  ends  that  are  bolted 
to  the  driving  gear  housing  and  that  an  outer  tube  is  to  be  forced 
over  its  smaller  end,  with  flanges  between  which  the  spring  saddle 
and  brake  support  are  to  be  held.  We  will  assume  that  the 
outside  diameter  of  the  tube  just  inside  the  wheel  bearing  is 
3*/2  inches.  Then,  allowing  a  stress  of  20,000  pounds  per  square 
inch  in  the  material  of  the  tube  we  have 

20,0007 
54,600  =  - 

c 
I 

—  =  2.73 
c 
The  section  modulus  is 

3.1416  (3.54  —  *4) 


64  150  — 


3.5  35.67 


2 

150  —  x* 

=  2.73 


35.67 

x*  =  52.62 
x  =  2.69 

If  nickel  sheet  tubing  is  used  a  slightly  higher  stress  can  be 
allowed  and  the  inside  diameter  made  equal  to  2Y*t  inches,  giving 
a  Y%  inch  wall. 

A  typical  heavy  worm  gear  axle,  that  used  on  the  Daimler 
motor  buses  operated  in  London,  is  illustrated  in  Figs.  206  and 
207.  These  buses,  when  laden,  weigh  13,440  pounds,  of  which 
8,960  pounds  are  carried  on  the  rear  axle.  They  are  fitted  with 
four  cylinder  Daimler-Knight  engines  of  4.6  inches  bore  by  4.4 
inches  stroke.  The  worm,  which  is  of  the  Lanchester  hour-glass 
type,  has  four  leads  and  the  wheel  29  teeth,  giving  a  reduction  of 
7l/4 :1.  The  distance  between  the  axes  of  worm  and  wheel  is 
7%  inches. 

It  will  be  noticed  that  the  axle  is  of  the  full  floating  type,  the 
cast  steel  wheels  running  on  the  outside  of  the  axle  tube  on  cylin- 


320 


THE  WORM  DRIVE. 


THE  WORM  DRIVE. 


321 


drical  roller  bearings.  Connection  between  the  axle  driving  shafts 
and  the  wheel  hub  is  made  by  bolted  on  caps.  The  tread  of  the 
rear  wheels  is  69  inches  and  the  distance  between  spring  centres 
50  inches.  The  rear  axle  shafts,  which  are  made  of  high  tensile 
nickel  steel,  have  an  effective  diameter  of  1?4  inches.  Both  ends 
of  the  driving  axles,  where  they  fit  into  the  driving  couplings, 
are  upset. 

The  worm  and  wheel  are  carried  by  a  removable  gear  carrier 
with  its  own  radial  and  thrust  bearings.  The  whole  differential 
can  be  removed  through  the  top  opening  after  the  axle  shafts 
have  first  been  withdrawn  and  to  this  end  it  is  not  necessary  to 
first  remove  the  bearing  caps  which  are  held  by  long  through 
bolts.  The  differential,  it  will  be  seen,  is  of  the  two  pinion  type 


FIG.  207. — SECTION  THROUGH  WORM  GEAR  OF  DAIMLER  Bus  AXLE. 

which  has  also  found  some  favor  in  this  country  on  account  of 
its  economical  manufacture.  Brake  support  and  spring  seat  are 
in  a  single  casting.  A  notable  feature  is  the  large  capacity  of  the 
central  housing.  There  is  no  stuffing  box  inside  the  axle  tubes  so 
the  lubricant  can  work  right  out  to  the  hub  bearings,  but  a  pack- 
ing is  provided  at  the  inner  end  of  the  wheel  hub  to  prevent  oil 
working  onto  the  brake  surfaces. 

In  American  practice  the  housings  for  heavy  worm-driven  axles 
are  generally  made  of  .steel  castings,  either  in  a  single  piece  ex- 
tending from  hub  to  hub,  or  in  three  pieces  with  bolted  joints 


322  THE  WORM  DRIVE. 

between  the  central  casing  and  the  spring  seats.  All  three  types 
of  axles,  full  floating,  three-quarter  floating  and  semi-floating, 
are  manufactured.  For  the  latter  the  advantage  is  claimed  that 
lateral  shocks  on  the  wheels  do  not  impose  nearly  such  heavy 
loads  on  the  outboard  bearings  as  in  full  floating  axles.  The 
Hotchkiss  drive  is  very  popular  with  the  makers  of  these  axles. 
This  requires  a  substantial  fastening  of  the  springs  to  the  axle, 
and  to  facilitate  this,  those  portions  of  the  axle  housing  to  which 
the  springs  are  secured  are  cast  of  square  cross  section,  instead 
of  being  made  round.  In  the  case  of  three-quarter  and  full  float- 
ing axles,  steel  tubular  members  are  inserted  into  the  cast  hous- 
ing, extending  close  up  to  the  differential  housing  and  being  sup- 
ported by  internal  flanges  or  bushings.  These  tubular  members 
extend  beyond  the  cast  housing  and  carry  the  bearings  on  which 
the  wheels  are  mounted.  Such  cast  steel  axles  are,  of  course,  of 
very  considerable  weight.  A  certain  design  of  full  floating  axle 
for  a  3l/2  ton  truck  weighs,  with  hubs  and  brake  drum,  1200 
pounds. 


CHAPTER  XI. 


THE  CHAIN  DRIVE. 

Transmission  by  means  of  chains  and  sprockets  is  now  very 
little  used  on  pleasure  cars,  but  is  still  found  on  commercial 
vehicles.  The  chain  possesses  the  advantage  of  a  slightly  greater 
flexibility  than  the  shaft  drive,  hence  it  tends  to  protect  the 
motor  and  tires  against  shocks  due  to  too  rapid  engagement  of 
the  clutch,  road  shocks,  etc.  When  kept  clean,  oiled  and  prop- 
erly adjusted,  the  chain  is  a  very  efficient  means  of  power  trans- 
mission. The  trouble  with  it  on  automobiles  is  that  it  is  usually 
exposed,  and  grit  soon  finds  its  way  into  its  numerous  bearing 
joints,  causing  rapid  wear.  In  order  to  keep  the  chain  at  its 
best  operating  efficiency  for  any  length  of  time,  it  is  necessary 
to  enclose  it  in  an  oil  tight  case  and  run  it  in  oil.  The  design 
of  a  light  chain  case  which  shall  hold  oil,  not  rattle  and  permit 
of  ready  inspection  of  the  chains  and  adjustment  of  their  tension 
is  a  rather  difficult  problem,  and  the  different  designs  of  cases 
evolved  do  not  seem  to  be  entirely  satisfactory.  In  the  centre 
or  single  chain  drive,  sometimes  used  with  light  pleasure  cars, 
and  particularly  with  friction  driven  cars,  the  difficulty  of  keep- 
ing an  exposed  chain  in  good  working  condition  is  especially 
great,  since  it  is  located  directly  in  the  path  of  splashing  mud 
and  water  from  the  wheels. 

Construction  of  Chains. — The  only  type  of  chain  used  for 
automobile  propulsion  is  the  roller  chain,  which  is  one  form  of 
the  general  class  known  as  machine-made  chains.  The  chain 
(Fig.  208)  consists  of  two  sets  of  links,  inner  and  outer,  re- 
spectively, each  set  of  one  kind  being  joined  to  two  sets  of  the 
other  kind  by  means  of  a  bushing  and  a  rivet  for  each  joint. 
The  bushing  serves  to  hold  the  pair  of  inner  links  the  proper 
distance  apart,  and  the  rivet  has  both  of  the  outer  links  riveted 
to  it.  In  passing  over  a  sprocket  the  rivet  turns  inside  the 
bushing  through  an  angle  which  is  equal  to  360  degrees  divided 
by  the  number  of  teeth  in  the  sprocket,  first  in  one  direction 

323 


324 


THE  CHAIN  DRIVE. 


and  then,  as  it  leaves  the  sprocket,  in  the  other.  It  is  this  mo- 
tion of  the  joints  which  is  responsible  for  the  wear  on  chains, 
and  as  the  motion  is  less  the  greater  the  number  of  teeth  in  the 
sprocket  the  advantage  of  using  large  sprockets  is  obvious. 

The  bushing  is  surrounded  by  a  roller  which  contacts  with  the 
sprocket  teeth.  Hence  the  contact  between  the  chain  and  the 
sprocket  is  a  rolling  contact  and  the  sliding  takes  place  between 
the  bushing  and  roller  and  between  the  bushing  and  pin.  The 
rivets  are  generally  made  of  nickel  steel  and  the  bushings  and 
rollers  are  hardened. 

Capacity  of  Roller  Chains. — The  permissible  working  ten- 
sion of  a  roller  chain  increases  substantially  as  the  square  of 
the  pitch,  because  both  the  pin  diameter  and  the  bushing  width 


^           1            ^ 

f  — 

^^ 

•\ 

\ 

^v 
xv?? 

^ 

^ 

'/ 

\\\\\\\\X 
^<SXX^\ 

^ 

i 
1 

^/ 

v^. 

^  p^^ 

^ 

FIG.  208— ROLLER  CHAIN. 

increase  with  the  pitch,  and  the  product  of  these  two  factors 
is  the  joint  area  to  which  the  working  load  must  be  proportional. 
Hence,  from  the  standpoint  of  strength  it  is  advantageous  to 
use  a  large  pitch.  On  the  other  hand,  since  the  diameter  of  the 
sprocket  is  limited  by  considerations  of  ground  clearance  re- 
quired, the  number  of  teeth  in  the  sprocket  is  inversely  propor- 
tional to  the  pitch,  and  since  the  angular  motion  at  the  joints 
is  inversely  proportional  to  the  number  of  sprocket  teeth  it  is 
directly  proportional  to  the  pitch.  Hence,  by  increasing  the 
pitch  we  reduce  the  unit  bearing  pressure,  but  increase  the  mo- 
tion at  the  bearings.  A  chain  of  smaller  pitch  operates  more 
quietly  and  has  a  longer  length  of  life  provided  the  tension  on 
it  is  not  too  high.  Roller  chains  for  automobiles  are  commer- 


THE  CHAIN  DRIVE.  325 

daily  made  in  pitches  varying  from  ^  inch  to  2  inches,  in  V^ 
inch  gradations,  and  each  pitch  is  made  in  several  different 
widths  of  rolls. 

The  Diamond  Chain  and  Manufacturing  Company  recommend 
the  following  sizes  of  chains  for  commercial  vehicles  of  different 
capacities : 

Pitch,  Width,  Roller  Diameter, 

Tons.  Inches.  Inches.  Inches. 

%  1  %  9-16 

%  -. 1  %  % 

1  114  %  % 

1%  1%  %  % 

2  1%  %  % 

2V2  and  3 !%•  1  % 

4        1%  1  1 

5  and  over    2  1^4  1% 

These  are  the  largest  sizes  used  in  practice,  and  it  is  not  un- 
common to  find  chains  several  sizes  smaller  than  those  recom- 
mended on  trucks  of  a  given  capacity. 

In  laying  out  a  chain  drive  for  a  commercial  vehicle  the  aim 
should  be  to  make  the  chain  speed  as  high  as  possible,  because 
in  any  case  the  average  chain  speed  will  be  moderate  and  the 
higher  the  chain  speed  the  less  the  tension  in  the  chain  for  a 
given  horse  power  transmitted.  The  large  sprocket  wheel  must 
clear  the  ground  by  about  7  inches,  hence  the  sprocket  pitch  diam- 
eter must  be  from  15  to  16  inches  less  than  the  wheel  diameter. 
The  pitch  diameter  of  the  front  sprocket  then  depends  upon  the 
gear  reduction  desired.  In  commercial  vehicles  fitted  with  solid 
tires  the  total  reduction  ratio  between  motor  and  rear  wheel  is 
generally  between  6  and  9.  It  is.  customary  to  make  the  two  re- 
ductions, at  the  bevel  gear  set  on  the  countershaft  and  at  the 
chains,  about  equal ;  hence  the  speed  reduction  by  the  chains  and 
sprockets  will  vary  between  2l/2  and  3.  This  gives  a  front 
sprocket  with  the  necessary  number  of  teeth  to  insure  proper 
operation.  Sprockets  with  less  than  ten  teeth  quickly  destroy 
the  chains.  Sprockets  with  12  to  13  teeth  give  tolerably  satis- 
factory service,  while  sprockets  with  15  teeth  or  more  are  most 
satisfactory. 

Chain  and   Sprocket  Calculations. — The  pitch   diameter  of 
a  sprocket  for  roller  chains  may  be  found  by  means  of  the  fol- 
lowing equation : 
P 

A>  =  (59) 

180° 

sin 

N 
where  DP  is  the  pitch  diameter ;  P,  the  pitch  of  the  chain,  and  N 


326 


THE  CHAIN  DRIVE 


the  number  of  teeth  in  the  sprocket.    Denoting  the  diameter  of  the 
roller  by  d,  the  outside  diameter  of  the  sprocket  blank  is 

DP  +  d, 
and  the  bottom  diameter 

DP  —  d. 

The  distance  between  centres  of  sprockets  for  a  certain  number 
of  links  in  the  chain  may  be  found  by  means  of  the  equation 


L  =  P 


N        n  j8    I 

-  __(AT_M)_ 

22  180  J 


2  cos 


where  Z  is  the  number  of  links  in  the  chain;  N,  the  number  of 
teeth  in  the  large  sprocket;  n,  the  number  of  teeth  in  the  small 
sprocket,  and  j8,  the  angle  made  by  the  chain  with  the  line  of 
centres  (see  Appendix  to  Vol.  I).  This  equation  gives  the  dis- 
tance required  for  the  chain  to  run  tight  on  the  sprockets.  A 
slight  amount  of  slack  is  necessary  and  means  for  adjusting  the 
distance  between  centres  are  generally  provided.  The  distance 


FIG.  209— OFFSET  LINKS. 

between  centres  of  sprockets  must  not  be  less  than  one  and  one- 
half  times  the  pitch  diameter  of  the  large  sprocket.  Too  long 
chains  are  also  objectionable  because  of  the  whipping  effect  if 
the  chain  is  at  all  loose.  In  commercial  vehicle  practice  the  dis- 
tane  between  sprocket  centres  is  generally  made  equal  to  about 
twice  the  pitch  diameter  of  the  large  sprocket.  In  fixing  this 
distance  it  is  preferable  to  figure  on  an  even  number  of  links, 
because  although  the  use  of  so-called  offset  links  (Fig.  209) 
permits  of  an  odd  number,  this  practice  is  objectionable. 

Design  of  Sprocket  Wheels — Sprocket  wheels  are  made  from 
steel  plate,  drop  forgings  or,  in  some  instances,  cast  steel.  The 
larger  sprockets  are  practically  always  in  the  form  of  flat  rings 
which  are  generally  bolted  to  the  brake  drums.  Front  sprockets, 
on  account  of  their  smaller  size,  wear  faster  than  rear 
sprockets  and  should  be  deeply  case  hardened.  Front  sprockets 
also  are  sometimes  bolted  to  separate  hubs,  the  advantages 
of  this  construction  being  that  when  a  sprocket  is  worn  out 


THE  CHAIN  DRIVE 


327 


only  the  steel  disc  need  be  renewed,  and  that  a  lot  of  sprockets 
can  be  forced  over  a  mandrel  and  cut  at  one  time.  Referring 
to  Fig.  210  the  width  B  of  the  sprocket  is  made  equal  to  twenty- 
nine  thirty-seconds  the  width  A  of  the  chain,  and  the  sprocket 
teeth  are  chamfered  on  their  outer  ends  from  the  pitch  line  on,  so 
as  to  reduce  their  width  C  on  the  circumference  to  one-half  the 
width  of  the  chain,  the  centre  of  the  chamfering  radius  being  lo- 
cated on  the  pitch  line.  The  clearance  D  for  the  side  links  below 
the  pitch  line  must  be  nine-sixteenths  of  the  pitch  or  more. 
Sprocket  wheels  are  cut  by  means  of  formed  cutters,  different 
cutters  being  used  for  wheels  of  the  same  tooth  pitch  but  with 
different  numbers  of  teeth.  Care  must  be  exercised  to  get  the 
bottom  diameters  exactly  right  and  that  there  is  the  proper 
amount  of  clearance  between  the  teeth  a»d  the  rollers  as  the 
chain  runs  onto  and  leaves  the 
sprocket.  In  order  to  insure 
concentricity  of  the  sprocket 
and  its  hub  or  centre,  when  the 
two  parts  are  made  separate, 
the  sprocket  blank  should  be 
made  an  accurate  fit  over  a 
turned  portion  of  the  hub  or 
centre,  against  the  flange  to 
which  it  is  bolted.  From  four 
to  eight  bolts  are  used  in  se- 
curing the  front  sprocket  to 
its  centre  and  a  relatively 
larger  number  for  the  rear 
sprocket. 


FIG.  210. — SPROCKET  DIMENSIONS. 


Chain  Pull. — If  the  maximum  engine  torque  is  denoted  by 
T,  the  combined  speed  reduction  ratio  of  the  low  gear  in  the 
transmission  and  the  bevel  gear  set  by  r,  the  pitch  diameter 
of  the  sprocket  pinion  by  d  and  the  combined  efficiency  of  the 
low  gear  and  the  bevel  gear  set  by  e,  then  the  maximum  chain 
tension  is 


12  T  r 
:    100  d 


.(60) 


Suppose  we  have  a  three  ton  truck  fitted  with  a  four  cylinder 
4^x5  inch  motor  which  develops  a  low  speed  torque  of  165 
pounds  feet.  Suppose  the  low  speed  reduction  in  the  change  gear 
is  3.2  and  the  reduction  of  the  bevel  gear  set  3.  Then,  considering 
the  efficiency  of  the  change  gear  and  bevel  gear  set  together  to  be 


328 


THE  CHAIN  DRIVE. 


90  per  cent.,  the  maximum  torque  on  the  jackshaft  is 

165x3.2x3x0.90=1,395  pounds-feet. 

The  proper  size  of  the  chain  to  use  is  a  il/2  inch  pitch  I  inch 
width  of  roll.  With  a  36  inch  rear  wheel  the  limiting  pitch 
diameter  of  the  sprocket  wheel  is  about  21  inches,  hence  we 
could  use  45  teeth,  which  gives  a  pitch  diameter  of  21.49  inches, 
and  if  the  total  reduction  from  engine  to  rear  wheels  is  to  be, 
say,  9,  then  the  chain  and  sprocket  reduction  must  be  3  to  i  and 
the  sprocket  pinion  must  have  15  teeth.  This  will  make  the  pitch 
diameter  of  the  sprocket  pinion 


/_o-x  0=7.215  inches 


FIG.  211. — OVERHANGING  SPROCKET  PINION. 
Hence  the  maximum  tension  in  each  chain  would  be 


1395  X  12 
7-215 


=  2,321  pounds. 


Such  a  chain  has  an  ultimate  strength  of  from  18,000  to  21,000 
pounds,  and  therefore  has  a  factor  of  safety  of  about  8  when 
working  under  full  engine  load  on  low  gear. 

Overhanging  Sprockets— Owing  to  the  high  tension  in  the 
chain  under  low  gear  it  is  advantageous  to  place  the  jackshaft 
outboard  bearing  in  the  centre  plane  of  the  chain,  which  requires 
that  the  sprocket  be  made  bell-shaped  or  be  bolted  to  a  bell- 
shaped  centre.  If  an  ordinary  symmetrical  type  of  sprocket 
were  keyed  to  the  jackshaft  outside  the  bearing,  the  tension  in 
the  chain  would  impose  a  heavy  bending  moment  on  the  shaft, 


THE  CHAIN   DRIVE. 


329 


which  is  avoided  by  so  arranging  the  sprocket  and  bearing  that 
their  centre  planes  coincide.  This  is  illustrated  in  Fig.  211. 

Chain  Adjusting  Rods — The  chain  adjusting  rods,  also 
known  as  radius  rods,  serve  a  triple  purpose.  They  take  up  the 
reaction  due  to  the  chain  pull,  allow  of  adjusting  the  slack  in 
the  chain,  and  transmit  the  driving  thrust  or  braking  pull  from 
the  rear  axle  to  the  frame.  These  rods  must  be  jointed  at  both 
ends  so  as  to  permit  of  free  play  of  the  springs,  and  the  joint 
centres  should  preferably  lie  in  the  axes  of  the  sprockets,  so 
that  any  play  of  the  springs  will  not  affect  the  sprocket  centre 
distances. 

Fig.  212  shows  a  simple  form  of  radius  rod,  as  often  fitted 
to  light  commercial  vehicles.  At  the  forward  end  a  T-shaped 
fitting  surrounds  a  cylindrical  portion  of  the  jackshaft  bearing 
bracket  or  the  jackshaft  tube.  The  radius  rod  proper  consists 


FIG.  212.— SIMLPE  FORM  OF  RADIUS  ROD. 

of  a  tube  which  is  threaded  on  the  inside  at  both  ends,  having 
a  forked  connector  secured  into  it  at  the  rear  end  which  con- 
nects with  a  lug  formed  integral  with  the  brake  support  or  spring 
saddle  on  the  rear  axle.  The  forward  end  of  the  radius  rod  is 
connected  to  the  T  fitting  already  referred  to  by  means  of  a 
turnbuckle  whose  opposite  ends  are  threaded  right  and  left  re- 
spectively. It  is  obvious  that  by  turning  this  turnbuckle  the 
distance  between  the  two  hubs  at  the  end  of  the  radius  rod  can 
be  varied,  and  when  the  adjustment  has  been  made  the  turn- 
buckle  can  be  locked  by  means  of  the  check  nuts  provided. 

While  the  above  construction  serves  the  purpose  of  a  radius 
rod  in  a  way,  it  does  not  make  proper  allowance  for  angular 
motion  of  the  rear  axle  with  relation  to  the  plane  of  the  vehicle 
frame,  as  caused  by  road  irregularities.  In  fact,  with  radius 
rods  of  this  type  the  rear  axle  can  move  freely  only  in  such  a  way 
that  it  always  remains  parallel  to  the  frame.  Any  other  motion 


330  THE  CHAIN   DRIVE. 

entails  heavy  strains  in  the  rods  and  their  connections.  Besides, 
if  the  loaded  truck  were  running  on  a  laterally  inclined  road  sur- 
face, or  if  the  rear  axle  should  receive  a  lateral  shock,  as  in 
striking  a  curb  as  the  result  of  a  skid,  the  greater  part  of  the 
strain  would  be  taken  up  by  the  radius  rods,  and  these  would 
be  likely  to  be  injured.  These  lateral  strains  should  preferably 
be  taken  by  the  body  springs,  and  to  this  end  the  joints  of  the 
radius  rods  to  the  frame  and  rear  axle,  respectively,  must  be  of 
the  universal  type. 


FIG.  213. — RADIUS  ROD  DOUBLE  PIVOTAL  FORWARD  JOINT. 

Fig.  213  shows  the  front  end  of  a  radius  rod  which  has  a 
double  pivotal  joint  with  the  frame.  The  fitting  to  which  the 
radius  rod  is  connected  swivels  on  the  jackshaft  bearing  bracket 
or  housing,  and  the  rod  has  a  pivotal  connection  with  this  fit- 
ting. The  forward  end  of  the  rod  proper  is  provided  with  a  hub 
which  is  internally  threaded  to  receive  a  bushing  which  is 
threaded  left  handedly  on  the  outside  and  right  handedly  on  the 
inside.  The  bushing  receives  the  shank  of  a  T-shaped  con- 
nector fitting.  By  turning  the  bushing  by  means  of  a  wrench 
the  effective  length  of  the  radius  rod  can  be  increased  or  de- 
creased, and  after  the  adjustment  has  been  made  the  parts  can 
be  locked  in  position  by  means  of  a  clamp  screw  and  check  nut. 

Fig.  214  illustrates  a  spherical  joint  for  the  forward  end  of  a 
radius  rod.  The  turnbuckle  is  provided  with  a  head  whose 
upper  and  under  faces  are  turned  spherically.  The  upper  face 
of  the  head  bears  against  the  spherical  head  of  a  steel  button 
inserted  into  a  drill  hole  in  the  wall  of  the  fitting  on  the  jack- 
shaft  bearing  bracket,  and  against  the  under  face  of  the  head 


THE  CHAIN   DRIVE.  331 

presses  an  externally  threaded  ring  screwed  into  a  threaded 
recess  in  a  boss  formed  on  the  fitting,  which  ring  is  also  provided 
with  a  spherical  surface.  After  adjustment  has  been  made,  the 
nut  can  be  locked  in  position  by  means  of  a  clamp  screw,  and 
the  same  locking  means  is  employed  for  the 'threaded  shank  of 
the  turnbuckle. 

The  joint  of  the  radius  rod  to  the  rear  axle  may  also  be  of 
either  the  double  pivotal  or  spherical  type.  The  former  is  illus- 
trated in  Fig.  215.  A  lug  is  formed  on  the  hub  of  the  brake 
support  which  is  swiveled  on  the  rear  axle,  and  the  rear  end  of 
the  radius  rod  is  connected  to  this  lug  by  means  of  a  pin  which  is 
held  in  position  either  by  means  of  a  bolt  head  and  nut  or  a 
locking  pin,  as  shown  in  the  illustration.  A  spherical  joint  for 
the  rear  end  of  a  radius  rod  is  shown  in  Fig.  216.  One-half  of 


FIG.  214. — RADIUS  ROB  SPHERICAL  FORWARD  JOINT. 

the  socket  is  formed  in  the  spring  saddle,  and  the  other  half  in 
a  fitting  which  is  bolted  to  the  spring  saddle.  The  ball  is  pro- 
vided with  a  threaded  shank,  which  is  screwed  into  the  tubular 
rod  and  secured  by  a  lock  nut. 

In  Fig.  217  is  shown  a  spring  cushioned  radius  rod  as  used  on 
the  Bussing  motor  trucks  made  in  Brunswick,  Germany.  The 
rear  end  of  the  radius  rod  is  connected  to  the  brake  support  and 
the  forward  end  is  made  telescoping  and  surrounded  by  a  volute 
spring.  It  is  obvious  that  in  case  of  a  sudden  increase  in  the  chain 
pull,  as  in  letting  the  clutch  in  too  quickly,  the  volute  spring 
will  compress  and  the  radius  rod  shorten,  thus  cushioning  the 
drive. 

When  a  spherical  type  of  joint  is  used  at  the  rear  end  of 
the  radius  rod,  it  is  not  convenient  to  use  the  latter  as  a  torque 
member  to  take  up  the  brake  reaction.  In  that  case  the  brake 
reaction  has  to  be  taken  up  by  the  body  springs  by  connection  of 


332 


THE  CHAIN  DRIVE. 


the  brake  support  with  the  spring  seat,  or  the  brake  support  may 
be  linked  to  the  vehicle  frame. 

Calculation  of  Radius  Rods — The  radius  rods  act  as  com- 
pression members  or  columns,  and  their  dimensions  should  be 
calculated  accordingly.  The  maximum  chain  tension  can  be  cal- 
culated by  the  method  already  explained  (Equation  60).  Besides 
this,  the  rods  must  transmit  the  propelling  thrust  from  the  rear 
axle  to  the  frame.  This  propelling  thrust  can  be  figured  on  the 
basis  of  15  per  cent,  of  the  weight  of  the  vehicle  on  the  two 
rods,  for  extreme  cases.  But  since  the  rod  makes  an  angle  with 
the  frame,  the  thrust  in  the  direction  of  the  rod  is  greater  than 
the  propelling  thrust,  in  the  ratio  of  unity  to  the  cosine  of  this 
angle. 


FIG.  215. — RADIUS  ROD  DOUBLE  PIVOTAL  REAR  JOINT. 

Thus,  in  the  case  of  our  3  ton  truck  we  found  that  the  maxi- 
mum chain  tension  was  2,321  pounds.  The  maximum  propelling 
thrust  on  each  side  is  975  pounds,  the  weight  of  truck  and  load 
being  13,000  Ibs.  Assuming  that  in  the  full  load  position  of  the 
spring  the  radius  rods  make  an  angle  of  20  degrees  with  the 
frame,  the  thrust  along  them  will  be 

9-^-  =  i,  040  pounds, 
0.94 

and  the  total  pressure  on  each  of  the  radius  rods, 
2321  +  1040  =  3361   pounds. 


THE  CHAIN  DRIVE. 


333 


FIG.  216. — RADIUS  ROD  SPHERICAL  REAR  JOINT. 

The   necessary   section    can   be   determined   by   means   of   the 
equation 


_ 

S  — 


_4_1!\ 

25,000  r2) 


(Rankine's  equation  for  steel  columns  free  at  both  ends).  In 
this  equation  6*  is  the  unit  compression  stress;  P,  the  total  pres- 
sure on  the  column;  A,  the  cross  sectional  area;  r,  the  least 
radius  of  gyration  of  the  section,  and  /  the  length  of  the  rod  or 
column.  In  order  to  use  this  formula  it  is  necessary  to  assume 
a  section  and  determine  the  value  of  the  stress  S,  and  if  this 
figures  out  either  too  high  or  too  low,  to  make  a  new  assumption. 
Let  us  assume  that  the  centre  to  centre  distance  of  the  radius 
rod  in  the  3  ton  truck  is  40  inches;  that  the  rod  is  to  be  tubular, 


FIG.  217. — CUSHIONED  RADIUS  ROD. 


334  THE  CHAIN   DRIVE. 

of  iJ4  inches  outside  and  Y&  inch  inside  diameter.    Then 

A  -  0.6  square  inch, 

7  =  0.097, 

^  =  0.151, 
and  the  unit  stress 

S  =  3i36i  /     ,  _4_JN6??\  =  I5,  IOoXpounds  i>er  sq.  in. 
0.6    \      '25,0000.1517 

Assuming  the  outside  diameter  to  be  il/2  inches  and  the  inside 
i  inch,  the  unit  stress  figures  out  to  about  7,000  pounds  per 
square  inch.  With  these  figures  and  a  table  of  standard  tube 
sizes  a  suitable  tube  can  easily  be  selected,  since  the  stress  can 
be  allowed  to  reach  a  value  of  12,000  to  15,000  pounds  per  square 
inch.  Of  course,  if  the  tube  is  threaded  on  the  inside  the  dimen- 
sion at  the  bottom  of  the  thread  must  be  taken  for  the  effective 
inside  diameter  of  the  tube. 

Many  radius  rods  serve  also  as  brake  torsion  members,  and 
these  snould  also  be  calculated  as  to  the  torsional  strains  pro- 
duced in  them,  which  can  be  done  by  the  same  method  as  used 
for  calculating  the  torque  rod  of  bevel  and  worm  driven  axles. 
Such  radius  rods  are  generally  made  of  I  section,  often  with 
parts  of  the  web  left  out,  and  for  commercial  vehicles  they  are 
mostly  made  of  cast  steel. 

In  designing  radius  rods,  the  designer  should  look  to  it  that 
the  adjusting  members  are  readily  accessible.  Means  must  be 
provided  for  taking  up  all  play  between  adjusting  members,  as 
else  the  joints  will  be  quickly  worn  out  by  the  shocks  of  the 
drive.  Grease  cups  msut  be  provided  for  all  bearings,  even  those 
having  but  a  very  slight  motion. 

Effect  of  Spring  Play  on  Chain  Drive — In  Fig.  218  is 
shown  a  chain  drive  in  diagram  in  two  different  positions,  the 
springs  being  assumed  to  be  distended  and  compressed,  re- 
spectively. The  sprocket  pinion  is  supposed  to  have  fifteen 
teeth,  and  the  sprocket  wheel  forty-five.  The  distance  between 
centres  is  assumed  to  be  28  inches,  and  the  total  vertical  motion 
of  the  springs  6  inches.  By  using  these  figures  a  direct  com- 
parison with  the  bevel  gear  drive  is  possible,  although  in  one  re- 
spect this  comparison  is  not  on  the  proper  basis,  since  the  pro- 
peller shaft  of  a  shaft  driven  car  is  nearly  always  made  consid- 
erably longer  than  the  radius  rod  of  an  equivalent  chain  driven 
car.  We  will  assume,  as  in  the  case  of  the  bevel  gear  drive,  that 
when  the  springs  are  compressed  the  line  of  centres  is  horizontal. 
Then  when  the  springs  distend,  the  line  of  centres  moves  through 
an  angle  a  determined  by  the  relation 


THE  CHAIN  DRIVE. 


335 


28 
Referring  to  Fig.  218,  a  portion  of  the  chain  whose  length  is 


A  £  = 


360 


inches 


winds  up  on  the  sprocket  wheel  and  a  portion  whose  length  is 

IT  da, 

CD  —  —  —  inches 
360 

unwinds  fro*i  the  sprocket  pinion.  The  length  of  chain  between 
the  extreme  points  of  contact  on  the  two  sprockets  (E  B,  C  A} 
remains  the  same.  Since  the  length  of  chain  which  unwinds 
from  the  pinion  is  not  equal  to  that  which  winds  up  on  the 


FIG.  218.  —  DIAGRAM  ILLUSTRATING  EFFECT  OF  SPRING  ACTION  ON 
CHAIN  DRIVE. 

wheel,    if    we    assume    that    the    wheel    remains    stationary    the 
sprocket  must  turn  to  unwind  a  length  of  chain 

ir(D  — 


AB—CD= 


360 


inches. 


It  must  turn  in  the  forward  direction   when  the  springs  dis- 
tend and  in  the  backward  direction  when  they  compress. 
A  motion  of 


360 

on  the  circumference  of  the  sprocket  pinion  corresponds  to  an 
angular  motion 

Q--=D~d  'a  degrees. 
d 

It  will  be  seen  from  this  that  when  D  =  d  —  that  is,  when  the 
two  sprockets  are  of  the  same  size  —  the  spring  action  has  abso- 


336  THE  CHAIN  DRIVE. 

lutely  no  effect  on  the  drive,  and  the  effect  is  the  less  the  smaller 
the  difference  in  the  sizes  of  the  two  sprockets.  In  the  case  of  our 
example,  since  D  is  substantially  equal  to  18  inches  and  d  to  6 
inches,  and  a  =  12°  21',  the  angular  motion  of  the  sprocket  pinion 
corresponding  to  a  spring  play  of  6  inches  is 

12°  21'  =  24°  42' 


This  is  considerably  less  than  the  angular  motion  found  for 
the  case  of  the  bevel  gear  drive  with  single  universal  joint,  viz., 
37°  30'. 

The  above  analysis  brings  out  another  reason  for  making  the 
reduction  ratio  in  the  chain  drive  as  small  as  possible. 

Chain  Cases. — Chain  cases  are  made  of  sheet  steel,  cast  steel 
or^cast  aluminum.  A  design  of  chain  case  intended  for  a  high 
grade  pleasure  car  is  illustrated  in  Fig.  219.  The  housing  is  made 
in  two  main  parts.  The  upper  part  is  clamped  and  bolted  to 
the  radius  rod  and  the  lower  part  is  hinged  to  the  upper  part, 
the  hinge  being  at  the  rear  end.  The  parts  overlap  at  the  divid- 
ing line  so  as  to  insure  a  substantially  oil-tight  joint.  In  the 
outer  side  of  the  case  circular  openings  are  left  which  are  large 
enough  for  the  sprockets  to  pass  through.  The  opening  for 
the  front  sprocket  is  closed  by  a  bowl-shaped  piece  of  sheet 
metal  with  double  rim  which  is  held  in  place  by  being  clamped 
between  the  two  parts  of  the  case,  whereas  the  opening  for  the 
rear  sprocket  is  closed  by  a  ring  bolted  to  one  of  the  parts  and 
making  a  tight  joint  with  the  brake  drum  by  means  of  a  felt 
ring  in  a  suitably  formed  groove.  There  is  an  inspection  hole 
in  the  upper  part  which  is  closed  by  a  hinge  cover.  It  is  located 
near  the  front  sprocket  where  access  to  it  is  not  interfered 
with  by  the  driving  wheel. 

The  radius  rod  has  a  long  bearing  on  the  axle,  and,  of  course, 
is  rigid  in  the  transverse  direction.  The  upper  part  of  the  case  is 
securely  fastened  to  the  rod  at  various  points  of  its  length. 
Near  its  forward  end  the  radius  rod  forms  a  loop  spanning  the 
jackshaft  bearing  bracket.  The  bearing  bracket  is  surrounded 
by  a  yoke  made  in  halves  riveted  together,  with  guiding  shanks 
extending  in  the  direction  of  the  rod.  One  of  these  shanks  is 
surrounded  by  a  sleeve  having  a  threaded  seat  in  the  end  of  the 
rod.  In  order  to  get  the  yoke  and  the  threaded  sleeve  into 
place  the  two  bearings  for  these  parts  in  the  radius  rod  have  to 
be  made  with  separate  caps. 

A  form  of  cast  steel  chain  case  is  illustrated  in  Fig.  220.     It 


THE  CHAIN   DRIVE. 


337 


338  THE  CHAIN  DRIVE. 

is  made  in  quarters,  as  shown,  and  bolted  together.  The  case 
also  serves  as  a  radius  rod  and  brake  support  and  is  strength- 
ened for  these  purposes  by  ribs  and  bosses  suitably  located.  The 
chain  tension  is  adjusted  by  means  of  an  eccentric  plate  sur- 
rounding the  bearing  housing  and  secured  to  the  casing  by  means 
of  cap  screws.  The  joint  between  the  eccentric  plate  and  the 
bearing  housing  is  of  the  ball  and  socket  type,  so  as  to  avoid 
straining  the  case. 
A  similar  adjustment  has  been  proposed  in  which  a  single 


FIG.  220. — CAST  STEEL  CHAIN  CASE. 

eccentric  is  used  with  worm  wheel  teeth  cut  on  its  circumference, 
with  which  mesh  the  teeth  of  a  worm  journaled  in  the  walls  of 
the  case.  Both  the  eccentric  and  the  worm  and  worm  wheel 
being  self-locking,  no  special  locking  device  is  required. 

Another  possible  method  of  chain  adjustment  in  connection 
with  a  case  consists  in  placing  a  square  bearing  block  around 
the  end  of  the  jackshaft  tube,  sliding  in  a  rectangular  groove 
in  the  case  and  adjusted  either  by  opposite  set  screws  through 
lugs  on  the  case  or  by  screw  wedges  back  of  the  bearing  block. 

Owing  to  the  difficulties  encountered  in  devising  chain  adjust- 
ing means  in  connection  with  chain  cases,  it  is  desirable  to  make 
the  range  of  adjustment  as  small  as  permissible.  It  must  be 
possible  to  adjust  the  centre  distance  enough  to  vary  the  chain 
length  one  complete  pitch.  This  necessitates  a  change  in  the 
centre  distance  of  substantially  one-half  a  pitch. 

Dead   Rear    Axles. — Dead   rear   axles   are   made   of   square 


THE  CHAIN  DRIVE. 


339 


rectangular  or  circular  cross  section,  the  rectangular  section 
predominating  in  recent  designs.  By  far  the  greatest  strain  on 
the  axle  results  from  the  vertical  bending  moment  due  to  the 
load  on  the  springs,  and  therefore  it  is  not  to  be  wondered  at  that 
a  section  is  employed  which  provides  greater  vertical  than  hori- 
zontal strength.  The  ratio  of  the  height  of  the  section  to  its 
width  varies  from  about  il/2  to  1^/4.  In  calculating  the  neces- 
sary section  of  the  axle  a  stress  of  15,000  pounds  per 
square  inch  can  be  allowed  for  hammered  medium  carbon  steel. 
Some  manufacturers  allow  20,000  pounds,  but  the  lower  figure 
is  better.  Thus,  let  L  be  the  load  supported  by  one  driving 
wheel  when  the  car  is  fully  loaded;  /,  the  distance  of  the 
spring  centre  from  the  wheel  centre ;  b,  the  width  of  the  axle 
section,  d  its  height,  and  r  the  ratio  of  d  to  b.  Then  the  bending 
moment  on  the  axle  is  L  /  and  the  resisting  moment  is 


6r 


Hence 


and 


Z/=- 


Qr 


(61) 


Having  found  the  height  of  the  section  the  width  is  found  by 
merely  dividing  by  the  assumed  ratio  r. 

Some  manufacturers  forge  the  spring  seats  integral  with  the 


FIG.  221. — DEAD  REAR  AXLE 


axle,  while  others  make  them  separate.  Beyond  the  spring  seat 
the  axle  is  made  of  round  section  to  form  a  seat  for  the  radius 
rod.  In  some  cases,  owing  to  lack  of  space  between  the  sprocket 
wheel  and  spring,  the  radius  rod  is  placed  on  the  inside  of  the 
spring.  However,  the  more  common  and  the  preferable  arrange- 
ment is  to  place  the  rod  close  to  the  chain,  so  that  the  bending 
moments  of  the  chain  pull  may  be  kept  as  low  as  possible.  That 
section  of  the  axle  which  serves  as  seat  for  the  radius  rod  or 
brake  support  is  always  limited  by  a  flange  at  the  inner  end,  and 


340 


THE  CHAIN   DRIVE. 


sometimes  also  at  the  outer  end,  in  which  latter  case  the  radius 
rod,  etc.,  must  be  made  with  a  separate  cap.  Beyond  this  por- 
tion comes  the  axle  spindle  which  usually  has  seats  for  two  anti- 
friction bearings  of  different  size,  and  at  the  end  a  threaded 
portion  over  which  screws  a  nut  which  holds  the  inner  races  of 
both  bearings  in  place,  a  spacer  being  placed  between  the  two 
inner  races.  A  typical  rear  axle  is  illustrated  in  Fig.  221. 

The  Jackshaft — In  the  earlier  cars  with  side  chain  drive  the 
bevel  gear  set  and  differential  on  the  jackshaft  were  usually  en- 
closed in  the  rear  part  of  the  change  gear  box,  and  Oldham 
couplings  were  inserted  in  the  two  halves  of  the  jackshaft.  How- 
ever, it  has  now  become  the  common  practice  to  make  the  jack- 
shaft  of  the  same  general  form  as  a  bevel  gear  driven  rear  axle, 


FIG.  222. — JACKSHAFT  END  AND  SUPPORT. 

using  either  a  pressed  steel  or  built-up  housing  which  extends 
across  the  frame  and  is  supported  from  the  frame  side  members. 
The  change  gear  case  can  either  be  bolted  to  the  rear  axle  hous- 
ing, it  can  be  placed  somewhere  between  the  engine  and  the  jack- 
shaft,  or  it  can  be  combined  with  the  engine  into  a  unit  power 
plant.  The  first  arrangement  is  the  most  common.  The  same  as  the 
rear  axle,  the  jackshaft  may  be  made  either  full  floating  or  semi- 
floating;  that  is,  the  outboard  bearings  may  be  placed  either  in- 
side a  bearing  housing  secured  to  the  end  of  the  jackshaft  tube, 
or  they  may  be  placed  on  the  outside  of  the  tube.  Fig.  222 
shows  a  typical  design  of  a  jackshaft  end,  including  the  bearing 
bracket,  bearing  housing:,  radius  rod  end  and  sprocket  pinion. 


CHAPTER  XII. 


BEVEL-SPUR   GEAR,   INTERNAL   GEAR  AND   FOUR- 
WHEEL  DRIVES. 

There  are  three  forms  of  double  reduction  drives,  each  compris- 
ing one  pair  of  bevel  gears  to  effect  the  right-angled  transmis- 
sion between  the  longitudinal  propeller  shaft  or  drive  shaft  and 
a  transverse  shaft.  The  other  reduction  may  be  obtained  either 
by  means  of  chains  and  sprockets,  a  pair  of  spur  gears  or  a  pair 
of  spur  pinions  and  internal  gears.  Chain  drive  was  at  one  time 
very  common  for  motor  trucks  and  other  commercial  vehicles, 
but  has  lost  much  ground.  The  bevel  and  spur  gear  drive  has 
been  used  by  Renault  in  France  and  by  several  manufacturers 
in  England,  especially  on  so-called  subsidy  models,  the  subsidy 
regulations  barring  the  worm  drive.  In  this  country  it  is  used 
by  the  Autocar  Company.  The  internal  gear  drive  also  had  its 
first  extensive  application  abroad,  but  has  now  found  quite  a 
following  in  this  country. 


FIG.  223. — DIAGRAM  OF  BEVEL- SPUR  DRIVE. 

In  a  bevel  and  spur  gear  drive  the  whole  of  the  gearing  is 
enclosed  in  a  single  case  at  the  middle  of  the  rear  axle.  As 
shown  in  the  diagram  of  a  bevel  spur  drive,  Fig.  223,  the  power 
is  first  transmitted  through  the  bevels,  because  the  end  thrust 

341 


342 


BEVEL-SPUR  GEAR  DRIVES. 


on  the  bevel  gear  is  then  much  less  and  can  be  more  readily 
provided  for.  Large  bevel  gears  also  are  more  expensive  to 
produce  than  equivalent  spur  gears,  and  this  is  probably  another 
reason  why  the  power  is  transmitted  through  the  bevel  gear  set 
first.  The  greater  part  of  the  reduction  is  obtained  by  means 
of  the  spur  wheels,  because  the  spur  gear  is  concentric  with  the 
axle  and  can  be  of  considerable  diameter  without  interfering 
with  anything.  While  it  would  be  possible  to  have  the  shaft 
carrying  the  bevel  gear  and  the  spur  pinion  in  the  same  hori- 
zontal plane  as  the  rear  axle  axis,  it  is  generally  placed  con- 
siderably higher.  In  most  designs  the  axes  of  the  spur  pinion 
and  gear  lie  in  an  inclined  plane,  the  pinion  axis  being  generally 
forward,  sometimes  to  the  rear  of  the  gear  axis,  but  where  space 
permits  the  pinion  may  be  directly  above  the  gear.  The  gear 
carrier  principle,  so  successfully  employed  on  worm  and  bevel 
gear-driven  rear  axles,  has  also  been  applied  to  the  spur  gear- 
driven  axle.  In  one  or  two  English  designs  the  differential  gear 


FIG.  224. — KARRIER  BEVEL- SPUR  DRIVE. 


is  mounted  on  the  intermediate  shaft  and  the  power  is  trans- 
mitted to  the  rear  axle  shafts  by  two  pairs  of  spur  wheels.  This 
has  the  advantage  that  a  smaller  differential  gear  will  do,  but  the 
disadvantage  that  two  pairs  of  spur  wheels  are  necessary  goes 
a  long  way  toward  nullifying  it. 

Arrangement  of  Gear  Relative  to  Axle — In  England,  where 
the  bevel-spur  drive  has  seen  its  widest  application,  it  is  used 
chiefly  in  connection  with  drop-forged  axle  housings  of  the  so- 
called  banjo  type.  Owing  to  the  irregular  shape  of  the  pear 


BEVEL-SPUR  GEAR  DRIVES. 


343 


housing  it  is  something  of  a  problem  to  properly  combine  the 
axle  and  gear  housings,  and  various  solutions  of  this  problem 
have  been  evolved.  Thus  the  Karrier  Company  places  the  central 
ring  of  the  axle  housing  horizontally,  as  shown  in  Fig.  224.  A 
top  gear  carrier  and  a  bottom  housing  are  secured  to  the  axle 
forging  by  screws.  This  makes  a  neat  and  handy  construction, 
but  has  the  disadvantage  that  the  material  in  the  ring  is  not  very 
favorably  disposed  to  support  vertical  bending  stresses.  To  make 
up  for  this,  an  unusual  amount  of  material  must  be  put  into  the 
ring,  as  may  be  seen  from  the  drawing.  In  the  Pagefield  axle, 
shown  in  Fig.  225,  the  ring  of  the  axle  housing  is  placed  vertically, 
and  this  axle  has  the  somewhat  unusual  feature  that  the  bevel 
gear  and  spur  pinion  are  located  to  the  rear  of  the  axle,  the  bear- 


FIG.  225. — PAGEFIELD  BEVEL-SPUR  DRIVE 

ings  for  the  shaft  on  which  these  two  gears  are  mounted  being 
supported  in  the  rear  cover,  while  the  bearings  of  the  bevel 
pinion  shaft  are  in  the  front  cover.  The  "ring"  of  the  axle 
housing  in  this  case  is  not  symmetrical  about  the  axis  of  the 
axle,  extending  higher  above  the  axis  than  below  it.  In  order 
to  combine  the  advantages  of  the  two  constructions  above  de- 
scribed, the  Wolseley  Motor  Car  Company  places  the  ring  of 
the  axle  housing  at  an  angle,  the  upper  part  being  tipped  back- 
ward (Fig.  226).  This  permits  of  the  use  of  a  symmetrical 
axle  forging  and  of  a  gear  carrier  supporting  all  of  the  gears 
of  the  drive,  so  that  the  latter  can  be  assembled  and  tested  before 
it  is  assembled  with  the  axle  housing.  It  will  be  observed  from 


344 


BEVEL-SPUR  GEAR  DRIVES. 


the  drawing  that  the  inclination  of  the  ring  toward  the  vertical 
is  not  great,  and  not  much  strength  is  sacrificed. 

Calculation  of  Spur  Gear  Drive — The  spur  gear  on  the  rear 
axle  is  made  of  as  large  a  diameter  as  consideration  of  ground 
clearance  required  will  permit.  The  pitch  diameter  will  vary 
roughly  from  about  10  inches  in  a  1-ton  truck  to  15  inches  in 
a  5-ton  vehicle.  For  trucks  of  3  tons'  load  capacity  and  over, 
4  diametral  pitch  teeth  may  be  used  for  the  spur  gears  and  5 
diametral  pitch  for  the  bevel  gears,  while  for  lighter  vehicles 
the  spur  gears  may  be  of  5  diametral  pitch  and  the  bevels  of  6. 
As  regards  materials,  the  same  steels  as  used  for  bevel  gears 


FIG.  226. — WOLSELEY  BEVEL-SPUR  DRIVE  AXLE. 


will  give  satisfaction,  that  is,  low  carbon  nickel  or  chrome  nickel 
steel,  case  hardened,  or  a  medium  carbon  chrome  nickel  steel, 
oil  hardened.  The  spur  wheel,  if  desired,  can  be  made  of  medium 
carbon  steel,  heat  treated,  as  it  is  naturally  stronger  and  sub- 
jected to  much  less  wear  than  the  pinion.  In  calculating  the 
necessary  width  of  face  of  the  spur  pinion  and  gear  the  Lewis 
formula  can  be  used,  allowing  a  stress  of  16,000  pounds  per 
square  inch  in  the  teeth  when  the  engine  drives  direct  and  de- 
velops its  full  torque.  This  may  seem  to  give  an  excessive  stress 
in  the  teeth  when  the  engine  drives  through  the  low  gear  at  full 
load,  but  it  must  always  be  remembered  that  the  Lewis  formula 
gives  a  considerably  higher  stress  than  actually  occurs. 

For  the  bevel  gear  teeth  the  stress  may  be  taken  somewhat 
lower,  say,  14,000  pounds  per  square  inch,  because  of  the  higher 
pitch  line  velocity  at  which  these  gears  run.  It  may  be  well  to 
illustrate  the  application  of  these  rules  by  a  practical  example. 


BEVEL-SPUR  GEAR  DRIVES.  345 

We  will  assume  that  a  three-ton  truck  is  to  be  fitted  with  a 

four-cylinder  4j4xSj4-inch  motor,  with  a  gear  reduction  of  8:1. 

Figuring  on  a  maximum  brake  m.e.p.  of  85  Ibs.  p.  sq.  in.  the 
engine  torque  is 

4  x  sy4  x  4^4  x  454  x  85 

=  168  lbs.-ft. 

192 

Let  us  assume  that  the  layout  shows  that  the  pitch  diameter  of 
the  spur  wheel  can  be  about  13  inches.  Then,  since  it  is  cus- 
tomary to  use  4  diametral  pitch  in  such  cases,  the  gear  can  be 
made  with  52  teeth.  For  the  pinion  we  may  choose  14  teeth. 
This  number  is  about  the  smallest  it  is  advisable  to  use,  as  with 
a  lesser  number  the  teeth  are  too  weak  in  the  root.  As  the  total 
reduction  is  to  be  1 :8  and  the  spur  gears  give  a  reduction  of 
14:52  =  1:3.71,  the  reduction  ratio  of  the  bevel  gears  must  be 
8/3.71  =  2.15.  Hence  the  torque  on  the  spur  pinion  shaft  will  be 

2.15  X   168  =  361  lbs.-ft. 
This  pinion  has  a  pitch  diameter  of 

14 

—  =  3.5  inches 
4 

and  a  pitch  radius  of  1.75  inches,  so  the  tangential  force  on  the 
pitch  radius  is 

361   X  12 

=  2480  Ibs. 

1.75 

Now,  applying  the  Lewis  formula,  we  have 

2480  =  16000  X  0.785  X  f  X  0.072, 
hence 

2480 

f  = =  2.73,  say,  2^4  inches. 

16000  X  0.785  X  0.072 

The  bevel  wheels  will  have  a  diametral  pitch  of  5.  We  will 
choose  for  the  pinion  22  teeth,  in  which  case  the  gear  must  have 
47  teeth,  and  see  how  the  width  of  face  figures  out.  If  it  comes 
out  considerably  less  than  30  per  cent,  of  the  pitch  line  length, 
then  we  can  choose  a  smaller  number  of  teeth,  which  will  result 
in  a  greater  proportionate  face  width,  and  vice  versa. 

The  Lewis  formula  adapted  to  bevel  gears  is 

S  p  y  L 

w  =  (1  —  a3) 

3 

where  w  is  the  tangential  load  at  the  maximum  pitch  radius  of 
the  pinion. 


346 


BEVEL-SPUR  GEAR  DRIVES. 


S,  the  stress  in  the  teeth, 
p,  the  circular  pitch. 

y,  the  Lewis  constant  for  the  number  of  teeth. 
L,  the  pitch  line  length,  and 

a,  the  ratio  of  the  distance  from  the  cone  apex  to  the  inner 
and  outer  ends  of  the  teeth,  respectively. 
The  pitch  diameter  of  the  pinion  is 

22 

—  =  4.4  inches 

5 


FIG.  227.— AUTOCAR  BEVEL-SPUR  DRIVE,  TRANSVERSE  SECTION. 

and  that  of  the  gear 

47 

—  =  9.4  inches. 
5 


BEVEL-SPUR  GEAR  DRIVES.  347 

The  pitch  radii  arc  equal  to  half  these  values,  viz.,  2.2  and  4.7 
inches,  and  the  pitch  line  length 


L  =    \2.22  +  4.72  =  5.09  inches. 

For  the  tangential  force  on  the  pinion  pitch  line  radius  we  get 
168  X   12 

=  917  Ibs. 

2.2 


FIG.  228. — AUTOCAR  BEVEL- SPUR  DRIVE,   LONGITUDINAL   SECTION. 


Therefore,  inserting  values  in  the  modified  Lewis  formula,  we 
have 

14000  X  0.63  X  0.093  X  5.09 
917  =  _____ (1  —  a3) 


348  BEVEL-SPUR  GEAR  DRIVES. 

3  X  917 

1  _  aa  = . -  =  0.659 

14,000  X  0.63  X  0.093  X  5.09 

a3  =  0.341 

a  =  0.7 

That  is,  the  distance  from  the  apex  of  the  cone  to  the  inner 
end  of  the  pinion  teeth  must  be  0.7  the  distance  from  the  apex 
to  the  outer  end  of  the  teeth.  Therefore,  the  face  width  must 
be  0.3  times  the  pitch  line  length  or 

0.3  X  5.09  =  1.527  —  say,  l*/2  inches. 

Figs.  227-8  illustrate  the  Autocar  bevel-spur  drive  which 
is  used  on  moderate-sized  commercial  vehicles.  The  inter- 
mediate shaft  with  which  the  bevel  gear  and  spur  pinion  are 
formed  integral,  is  located  directly  above  the  axle  and  is  car- 
ried in  two  roller  bearings  which  can  be  adjusted  endwise 
to  obtain  a  proper  mesh  of  the  bevel  gears.  Driving  keys  are 
used  for  the  spur  wheel,  which  is  bolted  to  the  flange  of  the 
differential.  The  short  shaft  of  the  bevel  pinion  is  carried  in 
two  roller  bearings.  The  axle  construction  is  of  what  is  known 
as  the  double  banjo  type,  the  main  axle  housing  being  in  halves 
which  are  bolted  together  at  the  middle  in  a  vertical  plane. 
Over  the  two  large  openings  in  this  casing  are  bolted  a  gear 
carrier  and  a  rear  cover  plate.  All  of  the  gearing  is  carried 
by  the  gear  carrier,  and,  therefore,  all  adjustments  can  be  made 
before  the  axle  is  assembled. 

Internal  Gear  Drive — While  the  bevel  and  spur  gear  drive 
as  now  designed  involves  the  use  of  a  live  axle,  the  internal 
gear  drive  is  used  in  conjunction  with  a  dead  axle.  On  the 
ends  of  this  dead  axle  the  driving  wheels  are  mounted,  and 
each  wheel  is  fitted  with  an  internal  gear  with  which  meshes 
a  spur  pinion  on  the  end  of  a  differential  countershaft.  This 
latter  is  designed  along  the  lines  of  a  live  rear  axle,  with  a 
gear  housing  at  the  middle  containing  the  differential  and 
bevel  driving  gears,  from  which  extend  the  differential  shafts, 
sometimes  surrounded  by  tubes.  The  shafts  connect  to  the 
differential  gear  at  their  inner  end  and  carry  a  spur  pinion 
each  at  their  outer  end.  The  countershaft  may  be  located 
either  directly  in  front  or  to  the  rear  of  the  dead  axle  or 
carrying  member  and  is  supported  at  the  middle  by  connection 
to  that  member.  If  the  driving  member  is  located  in  front 
of  the  carrying  member  the  bevel  gear  on  the  differential  must 
be  located  to  the  left  of  the  pinion;  in  the  opposite  case  it 
must  be  located  to  the  right  (assuming  the  engine  to  turn  right- 
handedly,  as  usual). 


BEVEL-SPUR  GEAR  DRIVES.  349 

As  in  the  bevel  and  spur  wheel  drive,  the  greatest  reduction 
is  obtained  by  means  of  the  second  set  of  wheels.  Ground 
clearance  is  not  such  an  important  consideration  near  the  wheels 
as  at  the  middle  of  the  chassis,  and  the  internal  gear  crown 
can  be  made  of  considerable  diameter.  The  pitch  diameters 
vary  roughly  from  12  inches  in  the  lighter  trucks  to  14  in 
the  heavier  ones.  As  regards  pitches  and  gear  materials,  what 
was  said  in  connection  with  the  bevel  and  spur  drive  applies 
here  also.  The  bevel  gear  set  at  the  middle  of  the  axle  can  be 
designed  on  the  same  basis  as  for  a  bevel-spur  drive;  that  is, 
about  14,000  Ibs.  p.  sq.  in.  can  be  allowed  with  case-hardened 
nickel  or  chrome  nickel  steel.  As  the  internal  gears  are  gen- 
erally made  of  carbon  steel,  unhardened,  a  much  lower  stress  is 
allowed  in  these  gears,  about  8,000  Ibs.  p.  sq.  in. — the  calcula- 
tions being  based  on  the  maximum  engine  torque  directly  trans- 
mitted. One  other  reason  for  the  comparatively  low  stress 
allowed  in  the  internal  gear,  besides  that  above  mentioned,  is 
probably  that  the  internal  gear  cannot  be  enclosed  as  effectively 
as  gears  located  in  a  housing  at  the  center  of  the  axle  and  cannot 
be  run  in  oil.  Grit  is  apt  to  get  into  the  gear  and  accelerate  the 
wear,  to  reduce  which  the  tooth  unit  pressure  is  kept  low. 

Theoretically  the  internal  gear  is  somewhat  more  efficient  than 
a  spur  gear,  because  there  is  less  sliding  action  at  the  teeth  of  the 
internal  gear,  but  the  actual  difference  is  small. 

The  internal  gear-driven  rear  axle  presents  quite  a  few  prob- 
lems of  design  aside  from  the  proportioning  of  the  gears.  First 
among  these  is  that  of  the  carrying  member,  which  may  be  made 
of  solid  round,  tubular,  rectangular  or  I-section.  The  axle  ends 
must,  of  course,  be  turned  off  to  form  seats  for  the  bearings, 
and  as  a  motor  truck  axle  requires  a  large  lathe  to  handle  it,  the 
spindles  have  sometimes  been  made  separate,  and,  after  being 
machined,  shrunk  into  the  tubular  central  portion.  Foreign 
makers  use  parallel  bearings  in  the  wheels,  while  American 
makers  use  ball  or  roller  bearings.  Great  care  must  be  taken 
to  so  mount  the  internal  gear  ring  that  it  will  permanently  run 
true  with  the  axle,  in  order  to  keep  the  gear  quiet  and  efficient. 
It  seems  preferabk  to  secure  the  gear  ring  directly  to  a  flange 
cast  integral  with  the  wheel  hub,  but  usually  an  intermediate  piece 
is  employed  for  convenience  in  manufacture.  The  support  for 
the  gear  ring  usually  also  forms  the  brake  drum.  This  construc- 
tion permits  of  the  use  of  either  a  contracting  brake,  directly  over 
the  gear  ring,  an  expanding  brake  (by  extending  the  supporting 
flange  beyond  the  gear  ring),  or  both. 


350 


BEVEL-SPUR  GEAR  DRIVES. 


BEVEL-SPUR  GEAR  DRIVES.  351 

As  the  spur  pinion  overhangs  its  bearings  and  as  the  pinion 
usually  has  a  very  small  pitch  diameter,  there  is  a  heavy  load 
on  this  bearing,  for  which  adequate  provision  must  be  made  in 
the  selection  of  the  bearing  and  its  mounting.  The  load  can 
be  calculated  by  the  usual  method  for  determining  bearing  loads 
due  to  gear  tooth  reaction  and  the  problem  need  not  be  entered 
into  further.  Usually  the  pinion  shaft  has  its  bearing  in  a  disc 
secured  to  the  carrying  member  of  the  axle,  which  disc  serves 
also  as  brake  support  and  as  a  closure  for  the  gear  housing  or 
brake  drum.  As  the  latter  rotates  while  the  disc  remains  sta- 
tionary, an  oil-tight  joint  between  the  two  cannot  be  obtained. 
Dust  may  be  excluded  by  cutting  a  groove  in  the  rim  of  the  disc 
and  filling  it  with  fibrous  material  or  by  providing  the  disc  with  a 
flange  which  overlaps  the  drum  flange. 

As  the  bevel  gear  and  pinion  do  not  differ  much  in  size,  there 
is  considerable  end  thrust  on  both  of  them,  which  must  be  pro- 
vided for.  This,  too,  can  be  calculated  by  the  usual  methods. 

In  an  internal  gear  axle  all  of  the  load  due  to  the  weight  on 
the  springs  is  taken  by  the  carrying  member  which,  therefore, 
must  be  calculated  like  a  dead  axle.  As  the  differential  shafts  do 
not  transmit  the  full  rear  wheel  torque,  but  only  a  fraction  of 
that  torque  determined  by  the  reduction  ratio  of  the  internal 
gear  set,  they  can  be  comparatively  small  and  the  tubes  sur- 
rounding them  can  be  made  very  light.  These  tubes  serve  only  as 
housings,  obviating  the  need  for  packings  at  the  end  of  the  bear- 
ings on  the  differential  shafts,  and  in  some  cases  they  are  dis- 
pensed with. 

Four  Wheel  Drives — The  four  wheel  drive,  as  pointed  out 
in  a  previous  chapter,  is  especially  advantageous  for  military 
trucks  and  tractors  which  frequently  must  operate  away  from 
beaten  roads.  It  is  also  well  adapted  to  use  on  trucks  em- 
ployed in  certain  lines  of  commercial  work,  as,  for  instance, 
in  contracting  work,  where  the  truck  may  have  to  be  driven 
into  and  out  of  sand  pits  or  on  rain-softened  ground.  The  ad- 
vantage of  the  four-wheel  drive  for  tractors  or  for  trucks  in- 
tended to  haul  one  or  more  trailers,  is  obvious,  for  when  the 
machine  must  move  more  than,  its  own  weight,  more  than  the 
usual  percentage  of  its  weight  must  be  rendered  available  for 
traction  purposes.  Moreover,  with  the  four-wheel  drive  the 
load  may  be  evenly  divided  between  front  and  rear  wheels, 
whereby  the  load  on  any  one  wheel  is  kept  down  and  an  exces- 
sive overhang  of  the  frame  over  either  axle  is  avoided. 

The  problem  of  a  four-wheel  drive  consists  chiefly  in  com- 


352  BEVEL-SPUR  GEAR  DRIVES. 

bining  the  functions  of  steering  and  driving  in  a  single  axJ^. 
As  the  steering  wheels  swing  around  a  substantially  vertic.  1 
axis  for  steering,  a  universal  connection  between  the  whee  s 
and  the  propelling  mechanism  on  the  frame  is  necessary,  un- 
less the  motor  and  drive  are  both  supported  on  the  axle,  or  on 
that  part  of  it  which  swings  in  steering.  The  problem  is 
about  the  same  as  that  involved  in  the  design  of  front  wheel 
drives,  as  used  for  converting  horse  fire  trucks  and  on  certain 
other  types  of  special  vehicles. 

One  of  the  simplest  solutions  of  the  problem  consists  in 
the  use  of  an  electric  transmission,  with  an  electric  motor 
mounted  directly  on  each  steering  knuckle,  or  on  each  axle 
if  the  whole  axle  swings  in  steering.  Of  mechanical  solutions 
there  are  three  that  are  well  known.  The  first  involves  the 
use  of  a  fifth  wheel  adapted  to  turn  around  a  king-pin,  so  that 
in  steering  the  entire  axle  swings  around  its  centre,  instead 
of  steering  knuckles  swinging  aroung  knuckle  pins.  The 
power  plant  may  then  be  mounted  so  as  to  turn  with  the  axle, 
or  the  power  may  be  transmitted  to  the  axle  by  means  of  gear- 
ing of  which  one  member  is  located  concentric  with  the  king- 
pin. 

The  second  method  makes  use  of  a  train  of  bevel  gears,  of 
which  a  pair  of  intermediate  gears  is  mounted  concentric  with 
the  steering  knuckle  pin.  This  arrangement  has  some  im- 
portant advantages,  but  it  is  rather  complicated.  In  one 
French  design  of  a  four-wheel  driven  truck  employing  this 
construction  no  less  than  thirty-two  bevel  wheels  are  used  in 
the  drive  between  the  gear  box  and  the  four  wheels.  One  of 
the  good  points  of  this  type  of  steering  and  driving  axle  is 
that  the  pivot  steering  principle  is  employed,  which  is  pre- 
ferable to  the  fifth  wheel  principle  in  many  respects;  another 
is  that  as  the  bevel  gears  secured  to  the  road  wheels  swing 
around  the  knuckle  pivots,  no  irregularity  in  the  transmis- 
sion of  motion  is  introduced.  That  is,  whether  the  road 
wheels  are  in  the  straight-ahead  position  or  not,  the  trans- 
mission of  motion  from  the  tail  shaft  of  the  gear  box  to  the 
road  wheels  is  always  effected  at  a  constant  ratio,  there  being 
no  periodic  fluctuation  as  with  ordinary  universal  joints. 

In  the  third  construction  universal  joints  are  employed  to 
transmit  the  motion  from  a  shaft  concentric  with  or  parallel 
to  the  axle  to  a  pair  of  short  shafts  carried  by  the  steering 
knuckles  on  opposite  ends  of  the  axle.  These  three  shafts, 
viz.,  the  long  central  shaft  and  the  two  short  shafts  connected 


BEVEL-SPUR  GEAR  DRIVES. 


353 


to  it,  mar  be  either  concentric  with  the  axle,  in  which  case  the 
short  shafts  connect  to  the  wheel  hubs  through  driving  dogs, 
or  they  may  form  a  countershaft,  in  which  case  the  short 
shafts  carry  spur  pinions  which  mesh  with  spur  or  internal 
gear  crowns  on  the  road  wheels.  In  either  case  the  universal 
joint  centre  must  lie  in  the  axis  of  the  steering  knuckle  pin. 


FIG.  230.— PANHARD  BEVEL  GEAR  DRIVEN   STEERING  WHLEL. 

With  the  latter  construction  the  torque  on  the  universal  joint 
is  much  less  than  with  the  alternate  construction,  and  the  axle 
can  be  built  lighter. 

Bevel   Gear   Steering   Wheel   Drive— Fig.  230   is   a   vertical 
section  through  the  wheel  and  drive  of  a  Panhard  four-wheeJ 


354 


BEVEL-SPUR  GEAR  DRIVES. 


driven  truck.  Only  one  universal  joint  is  employed  on  this 
truck,  located  at  the  rear  end  of  the  gear  box,  on  a  short  cross 
shaft  which  is  driven  by  bevel  gears  from  the  gear  box  tail- 
shaft.  At  each  end  of  this  cross  shaft  is  a  bevel  gear  through 
which  it  drives  fore-and-aft  shafts  extending  to  the  front  and 
rear  axles,  there  being  four  of  these  shafts  in  all.  As  the  shaft 
housings  pivot  around  the  axes  of  the  cross  shafts,  no  uni- 
versal joints  are  required  to  compensate  for  the  spring  mo- 
tion. Each  of  the  fore-and-aft  shafts  at  its  outer  end  carries  a 
bevel  pinion  meshing  with  another  bevel  pinion  on  a  short 
cross  shaft  extending  through  a  housing  underneath  the  chas- 
sis spring,  which  at  its  other  end  carries  another  bevel  pinion 
meshing  with  a  bevel  gear  at  the  top  e«d  of  a  vertical  shaft 
concentric  with  the  steering  pivot.  The  bevel  pinion  at  the 


FIG.  231. — F.  W.  D.  COMBINED  STEERING  AND  DRIVING  AXLE. 


lower  end  of  this  shaft  meshes  with  a  bevel  gear  secured  im- 
side  the  enlarged  hub  of  the  road  wheel.  In  a  more  recent 
design  of  the  Panhard  Company,  some  of  the  intermediate 
bevel  gear  sets  are  replaced  by  helical  gears,  whereby  the  total 
number  of  gears  is  reduced. 

Live  Steering  Axle— A  combined  driving  and  steering  axle, 
in  which  a  universal  joint  is  placed  inside  the  forked  axle  end, 
is  manufactured  by  the  Front  Wheel  Drice  Auto  Co.,  Clinton- 
ville,  Wis.,  and  a  part  sectional  view  of  this  axle  is  shown 
herewith.  On  the  truck  of  this  concern  the  change  speed  gear 
is  located  at  the  middle  of  the  frame,  and  from  the  tail  shaft 
of  the  gearset  the  power  is  transmitted  by  a  silent  chain  to  a 
fore-and-aft  shaft  with  differential  gear  and  universal  joints. 
From  this  fore-and-aft  shaft  the  power  is  transmitted  to  the 
two  driving  axles  by  bevel  pinion  and  gear,  a  sufficiently  large 


BEVEL-SPUR  GEAR  DRIVES. 


355 


gear  reduction  being  obtainable  because  the  speed  is  already 
reduced  somewhat  by  the  silent  chain  connection  between  the 
gearbox  and  the  longitudinal  shaft.  Each  axle  contains  one 
differential  gear,  so  that  there  are  three  in  all  on  the  truck. 

Details  of  the  construction  of  the  steering  and  power  trans- 
mission  joint  are   shown   in  the  illustration.     The   steering 


FIG.  232. — JEFFERY  COMBINED  DRIVING  AND   STEERING  AXLE. 


knuckle  pivot  is  developed  into  a  spherical  joint  which  con- 
tains trunnions,  fully  enclosing  the  universal  joint.  This 
joint  is  of  compact  design,  and  as  it  has  to  transmit  only  one- 
fourth  of  the  power  of  the  engine  it  is  amply  large  for  its 
purpose. 


356  BEVEL-SPUR  GEAR  DRIVES. 

Internal  Gear  Steering  Wheel  Drive — A  four-wheel  drive  by 
internal  gears  has  been  used  on  Jeffery  trucks,  and  a  section 
through  the  combined  steering  and  driving  wheel  is  shown  in 
Fig.  232.  The  sliding  gear  transmission  is  placed  at  the  mid- 
dle of  the  frame  and  has  no  direct  drive.  The  propeller  shafts 
are  gear  driven  from  the  secondary  transmission  shaft,  this 
construction  bringing  the  forward  one  far  enough  to  one  side 
to  clear  the  engine,  which  is  also  mounted  slightly  to  one 
side  of  the  frame  centre.  Three  differentials  are  used  and 
both  axles  are  pivoted  for  steering.  The  cross  shafts  are  lo 
cated  above  the  springs  and  have  universal  joints  direct!} 
above  the  steering  pivots.  The  driving  pinion  is  supportec 
on  the  steering  knuckle  between  roller  bearings  on  opposite 
sides  and  meshes  with  an  internal  gear  ring  set  into  the  en 
larged  wheel  hub.  A  drum  for  an  external  brake  is  also  fitted 
to  the  wheel  hub,  and  against  its  inside  surface  bears  a  felt 
packing  designed  to  exclude  dust  from  the  gears. 


CHAPTER  XIII. 


BRAKES. 

The  automobile,  being  essentially  a  high  speed  vehicle,  re- 
quires powerful  and  dependable  brakes  for  its  safe  operation. 
Aside  from  the  fact  that  the  engine  is  occasionally  used  as  a 
brake  (as  described  in  Volume  1,  Chapter  XVII)  and  that  in 
cars  with  friction  drive  or  planetary  change  speed  gears  the  re- 
verse gear  may  be  used  to  retard  the  speed  or  bring  the  vehicle 
to  a  stop,  drum  brakes  are  invariably  used  on  automobiles. 
These  consist  of  a  steel  or  cast  iron  drum  secured  to  some  rotat- 
ing part,  either  the  road  wheels  or  a  part  in  permanent  driving 
connection  therewith,  and  an  expanding  or  contracting  member 
supported  by  the  vehicle  frame  or  axle  which  can  be  brought  into 
frictional  contact  with  the  rotating  member.  When  this  expand- 
ing or  contracting  friction  member  is  pressed  against  the  surface 
of  the  drum,  the  friction  created  tends  to  stop  the  drum  and  its 
connected  parts  from  revolving.  The  energy  dissipated  in  heat 
at  the  friction  surface  of  the  drum  is  withdrawn  from  the  kinetic 
energy  stored  in  the  moving  vehicle,  and  the  speed  of  the  vehicle 
decreases  as  its  store  of  kinetic  energy  is  depleted.  The  con- 
tracting and  expanding  brakes  are  shown  in  diagram  in  Fig.  233, 
the  black  circles  representing  the  brake  drums. 

Number  of  Brakes — In  several  States  of  the  Union  and  in 
most  foreign  countries  two  independently  acting  braking  systems 
are  required  by  law,  and  sometimes  it  is  stipulated  that  at  least 
one  of  these  braking  systems  must  act  directly  on  the  road 
wheels.  What  is  here  referred  to  as  a  braking  system  consists 
of  a  single  drum  and  frictional  member,  if  it  is  located  ahead  of 
the  differential  gear,  as  on  one  of  the  change  gear  shafts ;  and 
of  two  drums  and  frictional  members  when  located  beyond  the 
differential  gear,  as  on  the  wheel  hubs. 

In  horse  vehicles  the  brakes  are  generally  applied  to  the  wheel 
tires.  Automobiles  are  almost  invariably  fitted  with  rubber  tires, 
and  while  the  application  of  brakes  to  these  tires  would  un- 

357 


358 


BRAKES. 


doubtedly  prove  very  effective,  rubber  is  too  expensive  to  make 
this  practice  commercially  possible.  Therefore,  it  is  customary 
to  secure  a  metal  drum  to  the  road  wheels  on  which  the  friction 
members  act. 

Location  of  Brakes. — The  brake  drums  may  be  fitted  to 
either  the  rear  wheels  or  the  front  wheels.  Rear  wheel  braking 
has  the  advantage  that,  as  a  rule,  the  rear  wheels  support  much 
more  of  the  weight  of  the  car  and  the  load  than  the  front  wheels, 
and  since  the  limiting  brake  power  depends  upon  the  ground 
adhesion  of  the  road  wheeels,  which  in  turn  depends  upon  the 
weight  carried  by  the  wheels,  it  is  seen  that  rear  wheel  brakes 
have  a  greater  limiting  power  than  front  wheel  brakes.  Be- 


FIG.  233. — DIAGRAMS  OF  CONTRACTING  AND  EXPANDING  BRAKES. 


sides,  much  less  difficulty  is  encountered  in  making  connections 
from  the  operating  devices  on  the  frame  to  brakes  on  the  rear 
wheels  whose  planes  always  retain  the  same  position  relative  to 
the  frame,  than  to  brakes  on  the  pivotally  mounted  front  wheels. 
Front  wheel  brakes  have  the  advantage  that  an  application  of  the 
brakes  does  not  tend  to  cause  the  car  to  skid,  as  does  the  applica- 
tion of  rear  wheel  brakes — at  least  not  in  the  same  degree.  Front 
wheel  brakes  have  been  used  to  some  extent  in  England  and  on 
the  Continent,  but  are  practically  unknown  in  this  country. 

In  a  bevel  gear  driven  car  either  both  brakes  may  act  on  drums 
secured  to  the  rear  wheels  or  one  brake  may  act  on  drums  so 
located,  and  the  other  on  a  drum  located  back  of  the  change  gear 
box.  There  is,  however,  one  exception,  namely,  when  the  trans- 
mission is  located  on  the  axle,  in  which  case  both  brakes  must 


BRAKES.  359 

act  directly  on  the  wheels.  In  Europe  it  is  the  almost  exclusive 
practice  to  place  one  brake  close  to  the  gear  box  and  the  other 
on  the  wheels. 

In  one  respect  the  proper  location  for  the  brakes  is  as  close  to 
the  road  wheels  as  possible,  because  the  reaction  due  to  the  fric- 
tional  force  on  the  brake  surface  takes  effect  at  the  road  contact 
of  the  wheel,  and  the  closer  the  points  of  application  of  the 
braking  force  and  the  point  of  its  final  reaction  are  together, 
the  fewer  parts  are  subjected  to  strain.  With  brakes  on  the 
hubs  of  the  rear  wheels  only  these  wheels  are  subjected  to  the 
strain,  whereas  if  the  brake  is  located  back  of  the  change  speed 
gear  the  braking  force  has  to  be  transmitted  through  the  pro- 
peller shaft,  universal  joints,  bevel  driving  gear  set,  rear  axle 
shafts,  rear  wheel  driving  dogs  and  rear  wheels.  One  reason 
that  leads  some  designers  to  use  a  so-called  transmission  brake  is 
that  they  want  to  enclose  all  of  their  brakes,  which  compels  them 
to  use  the  expanding  type 'of  hub  brakes,  the  only  type  lending 
itself  to  complete  enclosure;  and  since  conditions  of  space  avail- 
able make  it  difficult  to  fit  two  internal  expanding  brakes  to  each 
wheel,  they  place  one  brake  back  of  the  change  speed  gear.  As 
regards  the  objection  to  the  transmission  brake  above  mentioned, 
they  argue  that  the  various  parts  which  have  to  transmit  the 
braking  force  must  be  designed  strong  enough  to  transmit  the 
maximum  propelling  force,  which  is  about  equal  to  the  maximum 
braking  force,  hence  these  parts  should  not  be  injured  by  the 
latter  force.  An  advantage  of  the  transmission  brake  is  that, 
since  the  braking  force  is  multiplied  by  the  rear  axle  driving  gear, 
a  great  retarding  effect  can  be  produced  with  a  comparatively 
small  operating  effort., 

The  transmission  brake,  however,  is  very  little  used  on  pleasure 
cars  in  this  country  at  present  and  is  constantly  losing  ground. 
There  are  three  arrangements  of  double  rear  wheel  brakes,  all 
in  practical  use,  viz.,  two  internal  brakes  acting  on  the  same  drum, 
one  internal  and  one  external  brake  on  the  same  drum,  and  two 
internal  brakes  on  concentric  drums. 

On  commercial  vehicles  with  side  chain  drive  it  is  the  practice 
to  place  one  set  of  brakes  on  the  rear  wheels  and  the  other  on  the 
ends  of  the  jackshaft.  If  the  worm  drive  is  used,  one  brake  may 
be  placed  on  the  transmission  shaft  and  the  other  set  on  the  rear 
wheels. 


360  BRAKES. 

Service  and  Emergency  Brakes.— One  set  of  brakes  is  gen- 
erally designated  as  the  service  brake  and  is  intended  for  all 
ordinary  occasions.  It  is  operated  by  means  of  a  pedal  or  foot 
lever,  because  the  driver  can  keep  one  foot  on  the  brake  pedal 
all  the  time  and  therefore  can  operate  such  a  brake  with  a  mini- 
mum of  effort.  The  other  brake  is  known  as  the  emergency 
brake  and  is  intended  for  use  only  in  case  the  service  brake  fails 
or  when  an  exceedingly  strong  braking  action  is  required.  This 
emergency  brake  is  generally  operated  by  a  hand  lever  located  at 
the  side  of  the  driver's  seat.  If  the  car  is  fitted  with  a  "trans- 
mission" brake,  the  latter  is  usually  the  service  brake. 

Calculation  of  Braking  Power.— The  emergency  brakes  at 
least  are  generally  made  sufficiently  powerful  to  slip  the  wheels 
of  the  car  on  dry  road  surface.  Assuming  that  six-tenths  of  the 
total  weight  of  the  car  and  load  rests  on  the  rear  wheels,  and  that 
the  ground  adhesion  is  0.6,  the  maximum  brake  force  is 
0.6*0.6  W  =  0.36  W. 

Suppose  that  the  car  is  traveling  at  a  speed  V  miles  per  hour 
=  1.466  V  feet  per  second.  Then  the  kinetic  energy  stored  up  in 
it  is 

jn±&VY_jvin_  (appr } 

2^  30 

Now  let  the  brakes  be  applied  so  as  to  lock  the  wheels  and  the 
car  be  stopped  after  running  a  distance  x.  Then 

0.36  ^*  =  J^2 

30 
and 


io.8 

This  equation  gives  the  minimum  theoretical  distance  in  which 
a  car  can  be  stopped,  provided  six-tenths  of  the  total  load  rests 
on  the  rear  wheels.  If  a  greater  proportion  of  the  load  is  carried 
by  the  rear  wheels  the  minimum  stopping  distance  will  be 
smaller.  It  will  be  seen  that  the  distance  is  proportional  to  the 
square  of  the  initial  speed. 

In  some  official  trials  held  by  the  Automobile  Club  of  America 
on  Riverside  Drive,  New  York  City,  in  May,  1902,  the  average 

y* 

distance  in  which  the  cars  came  to  a  stop  was  feet.    In  a 

6.7 

recent  unofficial  test  on  a  macadam  pavement  on  Kings  Highway, 
Long  Island,  New  York,  a  car  was  brought  to  a  stop  from  vari- 
ous speeds  in  distances  which  may  be  represented  by  the  ex- 


BRAKES.  361 

V2 

pression .     It  should  be  pointed  out  that  it  is  very  difficult 

17.4 

to  obtain  uniform  results  in  such  tests;  first,  because  the  results 
vary  with  the  gradient,  with  the  direction  and  strength  of  air 
currents  and  with  the  road  conditions,  and  second,  because  it  is 
practically  impossible  to  insure  that  the  driver  shall  shut  off  his 
power  and  apply  his  brakes  exactly  at  a  given  point  along  the 
road. 


Friction  of  Motion 

FIG.  234. 

Conditions  Insuring  the  Quickest  Stop — It  was  found  in  ex- 
periments made  by  the  Westinghouse  Air  Brake  Company 
that  railway  car  brakes  exert  the  greatest  retarding  effect 
when  applied  with  such  force  that  the  wheels  do  not  quite 
lock  but  continue  to  revolve.  This  same  condition  undoubted- 
ly exists  in  connection  with  automobile  brakes.  It  may  be  ex- 
plained on  the  grounds  that  the  friction  of  rest  is  greater  than 
the  friction  of  motion,  and  that  when  the  wheels  become  locked 
the  rolling  friction  of  the  wheel  on  the  ground  and  the  bear- 
ing friction  of  the  axle  and  propeller  shaft  cease. 

The  braking  effect  certainly  is  the  greatest  if  the  energy 
dissipated  in  friction  in  traveling  a  unit  distance  is  a  maxi- 
mum. Let  R  be  the  starting  resistance  of  the  wheel  to  slip- 
page on  the  road  (friction  of  rest)  and  r  the  resistance  of  the 


362  BRAKES. 

wheel  to  slippage  once  it  has  begun  (friction  of  motion). 
Also  let  D  be  the  wheel  diameter  and  d  the  diameter  of  the 
wheel  brake  drum.  Then  the  maximum  frictional  force  which 
can  be  applied  to  the  brake  drum  without  causing  the  wheel 
to  slip  is  n 

—  (R  —  a), 

d 

where  a  is  a  very  small  quantity.  While  the  car  travels  a 
unit  distance  the  brake  drum  circumference  moves  a  distance 
d 

—  in  its  rotation  and  the  energy  absorbed  at  the  brake  sur- 
D 

face  is  d        D 

—  x  —  (R  —  a)  =  R  —  a. 

D         d 

In  addition  to  this  we  have  the  energy  absorbed  by  the  rolling 
friction  at  the  road  contact  and  the  bearing  friction.  We  will 
denote  the  sum  of  these  two  frictional  forces,  both  referred 
to  the  wheel  rim,  by  B,  and  the  energy  absorbed  by  these  two 
resistances  while  the  car  moves  through  unit  distance  may 
also  be  represented  by  B.  Therefore,  the  total  energy  ab- 
sorbed while  the  car  travels  a  unit  distance  when  the  brakes 
are  on  but  the  wheels  are  not  locked  is  R  +  B  —  a. 

On  the  other  hand  when  the  wheels  are  locked,  after  slip- 
ping has  begun,  which,  of  course,  occurs  instantly,  the  only 
resistance  encountered  is  the  sliding  friction  r  of  the  wheel  on 
the  road.  The  energy  absorbed  in  unit  distance  due  to  this 
friction  is  also  r.  Hence  we  must  prove  that 

R  +  B  —  a  >  r. 

It  has  already  been  stated  that  the  friction  of  rest  R  is  greater 
than  the  friction  of  motion  r.  This  holds  good  under  all  or- 
dinary conditions  of  friction,  as  in  bearings,  etc.,  and  no  doubt, 
holds  true  in  connection  with  sliding  friction  between  rubber 
tires  and  road  surfaces.  Of  the  two  remaining  items  B  has  a 
definite  value  which  on  good  roads  is  from  4  to  5  per  cent  of 
the  sliding  friction.  The  item  a,  on  the  other  hand,  may  be 
made  practically  nil,  as  it  represents  the  margin  which,  if 
added  to  the  brake  friction  referred  to  the  wheel  circum- 
ference would  cause  the  wheel  to  lock.  Hence,  under  the  most 
advantageous  conditions  this  item  is  insignificant  and  the  re- 
tarding action  is  then  greater  than  that  due  to  locked  wheels 
by  the  sum  of  the  following  three  items:  The  rolling  friction 
of  the  wheels  on  the  ground,  the  bearing  friction  in  the  axle, 
propeller  shaft  and  transmission,  and  the  difference  between 


BRAKES.  363 

the  friction  of  rest  and  the  friction  of  motion  between  wheel 
and  road. 

Not  only  will  the  brakes  stop  the  car  quicker  when  they  are  not 
quite  locked  but  the  wear  and  tear  on  the  tires  is  greatly  reduced. 
It  would,  therefore,  be  a  great  adxantage  if  a  brake  could  be 
designed  by  which  the  wheels  could  not  possibly  be  locked  by  the 
driver  but  which  could  nevertheless  be  applied  to  such  a  degree 
as  to  come  very  near  to  locking  the  wheels. 

Determination  of  Dimensions — The  two  considerations 
which  determine  the  size  of  brake  drums  are  that  the  brakes  must 
be  powerful  enough  to  practically  slip  the  wheels,  and  the  radiat- 
ing surface  of  the  brakes  must  be  large  enough  to  prevent  undue 
heating  on  long  down  grades.  Besides,  the  larger  the  brake  sur- 
faces, the  longer  the  friction  linings  will  last. 

The  drums  of  hub  brakes  on  pleasure  cars  are  generally  made 
of  a  diameter  equal  to  35-45  per  cent,  of  the  wheel  diameter, 
while  in  heavy  motor  trucks  the  brake  drum  diameter  is  made 
as  high  as  55  per  cent,  of  the  wheel  diameter.  On  pleasure  cars 
the  hub  brakes  should  have  a  friction  surface  equal  to  1  square 
inch  per  15  pounds  of  car  weight;  the  transmission  brakes,  1 
square  inch  per  30  pounds  of  car  weight.  On  commercial  ve- 
hicles, the  hub  brakes  should  have  1  square  inch  per  30  pounds 
of  car  weight  loaded;  jack  shaft  brakes,  running  at  a  speed 
intermediate  between  engine  and  rear  wheel  speed,  1  square  inch 
per  85  pounds  of  car  weight,  loaded,  and  transmission  brakes 
of  commercial  vehicles  running  at  engine  speed,  1  square  inch 
per  175  pounds  of  car  weight,  loaded.  Considerable  latitude  is 
permissible  as  regards  the  relation  of  face  width  to  diameter  in 
transmission  brakes,  and  no  general  rules  can  be  given.  If  the 
brake  is  located  at  the  middle  of  the  frame  where  there  is  ample 
room  in  the  direction  of  its  axis,  it  is  usually  made  comparatively 
wide  and  of  small  diameter,  whereas  if  the  brakes  are  at  the  side 
of  the  frame,  where  space  in  the  axial  direction  is  limited,  the 
drum  diameter  has  to  be  made  somewhat  larger. 

Brake  Drums — The  drums  of  hub  brakes  are  now  almost 
invariably  made  of  pressed  steel  and  in  many  cases  the  brake 
drum  serves  also  as  the  loose  flange  of  the  artillery  wheels. 
The  thickness  of  the  metal  is  made  %  inch  for  cars  weighing 
with  load  up  to  1,800  pounds ;  fs  inch  up  to  4,000  pounds ;  y^ 
inch  up  to  7,000  pounds;  &  inch  up  to  12,000  pounds,  and  Y% 
inch  above  12,000  pounds.  If  the  brake  drum  serves  as  a  hub 
flange  it  is  generally  pressed  with  an  inner  cylindrical  flange 
fitting  over  a  machined  portion  of  the  hub.  In  this  case  the  drum 


364 


BRAKES. 


is  held  in  position  by  the  hub  bolts.  If  the  drum  is  not  part  of 
the  wheel  it  may  be  clamped  to  the  spokes  by  means  of  clips. 
A  typical  design  of  pressed  steel  brake  drum  is  shown  in  Fig. 
235. 

Contracting  Brakes — The  contracting  members  of  contract- 
ing brakes  are  either  made  in  the  form  of  bands  of  thin  rolled 
steel  encircling  nearly  the  whole  drum,  or  they  may  be  made  in 
the  form  of  two  sectors,  either  of  rolled  steel  or  of  cast  material 
— steel  or  malleable  iron.  The  contracting  members  are  generally 
lined  with  an  asbestos  and  wire  fabric,  of  which  there  are  several 
on  the  market — Raybestos,  Thermoid,  Non-Burn,  etc. — this  lining 


FIG.  235. — PRESSED  STEEL  BRAKE  DRUM. 


being  secured  to  the  metal  band  or  segment  by  means  of  copper 
rivets.  The  friction  coefficient  of  asbestos  on  steel  is  about  0.3. 
The  contracting  members  must  be  supported  in  a  substantial 
manner,  as  the  reaction  of  the  braking  force  must  be  taken  up 
by  the  support.  In  early  designs  of  band  brakes  it  was  cus- 
tomary to  fasten  one  end  of  the  band  to  the  support  and  exert 
a  pull  on  the  other  end.  This  gives  a  very  powerful  braking 
effect  for  one  direction  of  motion — the  forward  direction — be- 
cause the  friction  between  band  and  drum  tends  to  apply  the 
band  tighter  to  the  drum.  But  when  the  car  runs  backward, 
down  hill  for  instance,  the  friction  tends  to  unwind  the  band 


BRAKES.  365 

and   the   braking   effect   is    then    very    small.      Such    brakes    are 
known  as  single  acting  and  are  no  longer  used. 

In  order  to  obtain  a  double  acting  effect,  contracting  brakes  are 
now  always  anchored  directly  opposite  the  contracting  mechan- 
ism. Brake  segments  are  formed  with  eyes  for  the  anchorage 
joint,  and  steel  bands  have  a  fitting  riveted  to  them  which  serves 
the  same  purpose.  The  support  is  usually  a  bracket  secured  to 
the  rear  axle  tube,  and  in  a  few  cases  the  radius  rod. 


FIG.  236. — CONTRACTING   BAND   BRAKE. 

So  far  as  contracting  type  hub  brakes  are  concerned,  a  single 
style  of  contracting  mechanism  is  used  for  the  great  majority 
of  designs.  It  consists  of  a  floating  bell  crank  as  shown  in 
Fig.  236. 

One  end  of  the  brake  band  is  connected  by  means  of  a  riveted 
bracket  to  the  end  of  the  short  arm  and  the  other  end  connects 
through  a  short  link  to  the  fulcrum  of  the  bell  crank.  The 
operating  rod  is  connected  to  the  long  arm  of  the  bell  crank. 
The  link  is  hinged  to  the  free  end  of  the  brake  band  and  passes 
through  the  fulcrum  pin,  the  bell  crank  being  forked  at  the  lower 
end.  A  butterfly  nut  is  screwed  over  the  end  of  the  link  and 
provides  convenient  means  of  adjustment  for  wear.  The  adjust- 
ment is  locked  by  the  spring  surrounding  the  link,  which  forces 


366 


BRAKES. 


the  arms  of  the  bell  crank  over  the  flattened  end  of  the  wing 
nut,  thus  preventing  it  from  turning.  The  coiled  spring  at  the 
same  time  helps  to  release  the  band  when  the  pressure  is  taken 
off  the  brake  lever. 

There  is  one  other  form  of  contracting  mechanism  for  hub 
brakes,  consisting  of  a  short  double  armed  lever  with  pins  ex- 
tending laterally  from  the  ends  of  its  arms  to  which  the  ends 
of  the  brake  band  are  hinged,  and  an  operating  shaft,  rigidly 
supported,  extending  from  it  laterally  in  the  opposite  direction 
(Fig.  237). 


FIG.  237.— DOUBLE- 
ARMED  LEVER  CON- 
TRACTING MECH- 
ANISM. 


FIG.  238.— ADJUSTABLE 
BRAKE  BAND  SUPPORT. 


Releasing  Means—In  addition  to  providing  a  substantial 
support  for  the  brake  band  and  an  effective  contracting  mechan- 
ism, it  is  necessary  to  provide  means  which  will  prevent  dragging 
of  any  part  of  the  brake  band  when  released.  In  order  to  pre- 
vent dragging  near  the  point  of  anchorage,  a  portion  of  the  band 
extending  over  a  considerable  angle  on  both  sides  of  the  anchor- 
age may  be  left  unlined,  or  else  the  hole  in  the  anchoring  fitting 
may  be  made  oblong  in  the  radial  direction  so  that  the  brake 
band  can  move  outward  when  released.  Such  outward  movement 
is  insured  by  placing  a  spring  at  the  point  of  anchorage  soliciting 
the  band  radially  outward,  or  by  placing  stops  at  120  deg/ees 
(more  or  less)  on  either  side  of  the  point  of  anchorage  which 
limit  the  outward  movement  of  the  band  at  these  points  and 
thus  tend  to  distribute  the  clearance  evenly  around  the  circum- 
ference of  the  drum. 


BRAKES.  367 

The  contracting  mechanism  may  be  placed  on  top  of  the  drum 
or  on  the  forward  side  of  it.  The  latter  is  the  favorite  location, 
partly  because  it  brings  the  brake  connecting  rods  into  a  more 
convenient  level  and  partly  because  with  the  split  in  the  band  at 
the  side  of  the  drum,  mud  dropping  from  the  wheel  cannot  so 
easily  work  between  the  band  and  drum. 

Owing  to  the  fact  that  the  brake  band  is  firmly  supported  at 
one  side  only,  at  the  anchorage,  when  released  it  tends  to  drop 
on  to  the  drum  on  top  and  thus  drag.  In  order  to  prevent  this 
a  brake  band  carrier  is  usually  placed  fon  top  of  the  brakes.  In 
Fig.  208  this  takes  the  form  of  a  little  angle  piece  riveted  to 
the  brake  support  disc  and  extending  across  the  top  of  the  brake 
band  underneath  a  little  flat  spring  extending  circumferentially 
of  the  band  and  being  riveted  to  it.  When  the  brake  is  released 
the  spring  lifts  the  band  off  the  drum,  but  when  it  is  applied, 
the  spring  flexes  slightly  and  allows  the  band  to  come  in  contact 
with  the  drum.  Sometimes  three  of  these  brake  band  carriers 
are  used,  spaced  equally  around  the  circumference,  and  in  some 
designs  the  brackets  themselves  are  springs. 

The  band  supporters  are  not  adjustable  and  must  therefore  be 
very  accurately  made  and  fitted.  Besides,  if  some  means  of  ad- 
justment were  provided,  less  clearance  would  suffice.  An  ad- 
justable supporter  is  shown  in  Fig.  238.  A  threaded  pin  riveted 
into  the  brake  band  extends  vertically  upward  at  the  top  of  the 
brake  through  a  hole  in  an  angle  piece  secured  to  the  brake  sup- 
port disc.  A  coiled  spring  is  placed  on  top  of  this  angle  piece 
and  presses  against  a  castellated  nut  on  the  end  of  the  threaded 
pin. 

Contracting  Transmission  Brakes. — In  European  cars  the 
service  brake  is  generally  located  at  the  rear  end  of  the  change 
gear  primary  shaft  and  both  expanding  and  contracting  types  are 
used  at  this  point,  the  latter  being  perhaps  the  most  numerous. 
Most  of  the  contracting  brakes  have  cast  sectors,  and  these  are 
contracted  by  means  of  either  one  or  two  pairs  of  face  cams 
or  by  a  square  threaded  screw  and  nut  mechanism.  Continental 
manufacturers  generally  cast  four  or  five  circumferential  ribs 
on  the  brake  segments  (Fig.  239)  to  help  carry  off  the  heat  in 
making  long  descents.  The  brake  drum  of  a  transmission  brake 
is  generally  a  casting  keyed  to  the  rear  end  of  the  gear  box 
primary  shaft  and  often  has  two  lugs  cast  on  its  web  which 
form  part  of  the  universal  joint.  The  brake  segments  are 
anchored  to  the  gear  box  and  the  stops  and  supports  of  the 


368 


BRAKES. 


FIG.  239. — BRAKE  SEGMENT  WITH   COOLING  FLANGES. 

contracting  mechanism  also  are  secured  thereto.  Fig.  240  illus- 
trates a  design  of  contracting  transmission  brake  with  face  earn 
contracting  mechanism.  These  brakes  generally  have  metallic 
friction  surfaces.  A  transmission  brake  of  the  lever  operated 
band  type  is  illustrated  in  Fig.  241. 


Fir,.  240.— CONTRACTING  TYPE  OF  TRANSMISSION  BRAKE. 


BRAKES. 


369 


Stresses  in  Brake  Members — We  have  assumed  the 
maximum  braking  force  to  be  equal  to  36  per  cent,  of  the  totaJ 
weignt  of  the  car  and  load.  The  braking  force  being  produced 
on  two  wheels,  tnat  on  each  wheel  is  0.18  W.  Now  let  the  wheel 
diameter  be  D  and  the  brake  drum  diameter  d,  then  the  tan- 
gential force  on  the  circumference  of  the  brake  drum  is 

F=o.*£w 

d 

The  reaction  due  to  this  force  is  taken  up  in  the  brake  sup- 


FIG.  241. — CONTRACTING  BAND  TRANSMISSION   BRAKE. 

port.  In  Fig.  242,  F  represents  the  reaction  of  the  support  on 
the  brake  band.  Each  half  of  the  band  covers  an  angle  of  aboui 

165  degrees  =  ^~  *.    In  calculating  the  forces  on  the  brake  band 

use  is  made  of  the  method  developed  in  connection  with  band 
clutches,  the  band  brake  and  band  clutch  depending  upon  the 
same  principle.  We  found  (equation  19)  that  the  relation  be- 
tween the  initial  tension  Pi  on  the  band  and  the  pull  P  on  the 
anchorage  -is  such  that 


370 


BRAKES. 


where  e  is  the  base  of  the  natural  system  of  logarithms;  /  the 
friction  coefficient  and  6  the  arc  of  contact  between  band  and 
drum  in  circular  measure.  With  a  friction  coefficient  of  0.25 

and   an   arc  of  contact   for   each  half   of  the  band   of     —  *", 

12 

•/*    ft 

the  value  of  /  6  is  0.72,  and  the  value  of  e'  is  found  to  be; 
2.08.  (See  Fig.  36.) 


/ 

/\ 


T 

FIG.  242. — DIAGRAM  OF  FORCES  ON  A  BAND  BRAKE. 

In  Fig.  242  let  us  denote  the  tension  on  the  band  at  point  D 
by  x.    Then  the  tension  at  the  section  CC  just  ahead  of  the  point 

x 

of  anchorage  is  .     The  tension  at  the  section  BB,  just  be- 

2.08 

yond  the  point  of  anchorage,  is  -2—  -f  F  and  the  tension  at  tin 

2.08 

Doint  D  is 


-- 
2.08 

2.08 


BRAKES.  371 

Hence  the  tensions  at  the  two  ends  of  the  band  are  x  and 


£^5  -  respectively.    A  relation  between  these  two  forces  can 

2.08 

be  found  from  the  diagram  of  forces  acting  on  the  contracting 
bell  crank. 

It  will  be  seen  that  the  reaction  on  the  fulcrum  of  the  bell 
crank  must  be  equal  in  magnitude  and  direction  to  the  tension  at 
the  end  D  of  the  band,  and  the  dotted  line  KH  represents  this 
force.  This  reaction  is  the  resultant  of  the  forces  acting  on  the 
arms  of  the  bell  crank.  We  will  assume  that  the  brake  rod  con- 
necting to  the  vertical  arm  lies  in  a  horizontal  plane,  hence  the 
pull  on  this  rod  is  horizontal.  The  force  on  the  short  arm  of 
the  bell  crank  is  tangential  to  the  extreme  point  of  contact  of 
this  half  of  the  band.  This  enables  us  to  complete  the  diagram 
of  forces  KHI.  Ffom  this  we  see  that  with  this  particular  de- 
sign of  band  and  operating  bell  crank  the  tensions  at  the  two 
ends  of  the  band,  KH  and  KI,  are  equal.  Hence 


2.08 
3.326  x  =2.08  F 
x  =  0.624  F 
Inserting  the  value  of  F  found  previously  we  have 

*  =  0.624x0.18  —  W 
d 

The  diagram  also  enables  us  to  determine  the  proper  length 
for  the  effective  lever  arm  KG. 

In  order  that  the  operating  mechanism  may  be  in  equilibrium, 
the  moments  around  any  point  must  vanish.  Taking  moments 
around  the  fulcrum  K  — 

and 


Let  us  assume  the  case  of  a  car  weighing  with  load  3,000 
nounds,  and  let  the  ratio  of  wheel  diameter  to  brake  drum  dia- 
meter be  2.y2.  Then  the  reaction  F  on  the  brake  support  is 

0.18x2^x3,000  =  1,350  pounds, 


372  BRAKES. 

and  the  tension  on  each  end  of  the  band  is 

0.624  X  1,350  =  843  pounds. 

The  angle  between  the  forces  KH  and  KI  being  30  degrees,  the 
value  of  HI  is 

2  KI  sin  15°  =  2  X  843  X  0.259  =  436  pounds. 
Therefore,  the  effective  lever  arm  KG  should  be  to  the  effective 
lever  arm  KA  as  843  is  to  436 ;  in  other  words,  the  former  should 
be  about  twice  as  long  as  the  latter. 
We  now  have  the  following  results : 
Reaction  F  on  brake  anchorage,  1,350  pounds. 
Tension  on  each  end  of  the  band,  843  pounds. 
Tension  in  brake  rod,  436  pounds. 

These  are  extreme  values  and  are  hardly  likely  to  be  attained 
in  practice,  owing  to  the  fact  that  the  limiting  pressure  which 
the  driver  can  exert  on  the  brake  pedal  is  about  100  pounds,  and 
in  order  to  produce  a  tension  of  436  pounds  in  each  of  the  two 
brake  rods,  the  thrust  on  the  pedal  would  have  to  be  multiplied 
more  than  eight  times  by  the  leverage,  which  is  rather  a  higher 
leverage  than  is  obtainable  in  practice. 

The  value  of  the  force  F  on  the  brake  anchorage  permits  of 
calculating  the  necessary  size  of  the  laterally  extending  stud  or 
pin  and  of  the  bracket  which  carries  this  stud.  Thus,  let  the 
entire  overhang  of  the  anchorage  pin  be  2  inches,  so  that  the 
centre  point  of  the  band  overhangs  1  inch.  Then  the  bending 
moment  of  the  force  F  is  1,350  pounds-inches,  and 
TT  D3'  S 

=    1,350 

32 

Since  the  force  assumed  is  practically  the  limit  that  can  ever 
come  on  the  brake  support  we  can  make  the  stress  comparatively 
high,  say  20,000  pounds  per  square  inch.    We  then  have 
20,000  D3  =  13,750. 
D3  =  0.6875. 

7 
D  =  0.88  inch  —  say,  —  inch. 

8 

Other  parts  of  the  brake  mechanism,  such  as  the  brake  anchor- 
age bracket  and  the  contracting  lever,  can  be  calculated  for 
strength  in  a  similar  manner. 

Expanding  Mechanism — There  are  four  commonly  used 
means  for  expanding  the  sectors  of  internal  brakes,  viz.,  cam, 
toggle,  wedge  and  double-armed  lever  mechanisms.  The  cam  is 
probably  the  most  extensively  used.  Three  designs  of  expander 
cams  are  illustrated  in  Fig.  243.  The  symmetrical  cam  shown  at 


BRAKES. 


373 


FIG.  243. — EXPANDER  CAMS. 

A  has  flat  sides  and  semi-circular  ends,  and  its  small  diameter  is 
usually  one-half  its  big  diameter.  The  second  design,  B,  has 
practically  the  same  effect  as  the  first,  but  is  preferable  from  the 
standpoint  of  weight  economy,  having  some  useless  metal  cut  out. 
The  third  design,  C,  embodies  roller  cam  followers  carried  on  the 
ends  of  the  brake  segments,  the  idea  being  to  minimize  wear  of 
the  working  parts. 

The  segments  of  cam-operated  expanding  brakes  are  provided 
with  flat  wearing  surfaces  against  which  the  cams  bear,  and 
these  wearing  surfaces  and  the  cams  are  case  hardened.  The 
extreme  motion  provided  for  in  the  case  of  a  i4-i6-inch  drum 
is  usually  l/2  inch  for  the  end  of  each  segment. 


FIG.  244.— TOGGLE  EXPANDER  BRAKE. 


374 


BRAKES. 


Fig.  244  illustrates  a  Lrake  with  a  toggle  expanding  mechanism. 
The  ends  of  the  segments  are  connected  by  a  pair  of  toggle  links 
from  the  joint  of  which  runs  another  link  to  a  bell  crank  whose 
shaft  has  a  bearing  in  the  brake  supporting  bracket.  Sometimes 
one  or  both  of  the  toggle  links  are  made  adjustable.  The  toggle 
mechanism,  like  the  cams,  has  the  advantage  that  it  moves  the 
ends  of  the  brake  segments  comparatively  fast  at  first,  but  more 
slowly  as  the  segments  come  in  contact  with  the  drum.  Its 
mechanical  advantage  increases  as  the  segments  are  being  ex- 
panded, consequently  with  a  certain  effort  on  the  part  of  the 
operator,  the  segments  can  be  applied  to  the  brake  drum  with 
greater  force  than  if  the  mechanical  advantage  remained  con- 


FIG.  245.— WEDGE 
EXPANDER  MECH- 
ANISM. 


FIG.  246.— DOUBLE- 
ARMED  LEVER  EX- 
PANDER. 


stant.  The  toggle  mechanism  is  really  the  only  one  that  can  be 
properly  adjusted  for  wear  of  the  brake  lining,  by  adjusting  the 
length  of  the  toggle  links.  The  only  way  in  which  the  other 
mechanisms  can  be  adjusted  is  to  make  the  expanding  range 
considerably  larger  than  is  necessary  when  the  brake  lining  is 
new,  and  then,  as  the  lining  wears,  adjusting  the  operating  link- 
age outside  the  brake  drum. 

A  wedge  expander  is  shown  in  Fig.  245.  The  ends  of  the  seg- 
ments are  beveled  and  a  wedge  pivoted  to  a  cantilever  is  forced 
between  them.  The  double-armed  lever  mechanism  j>,s  applied 
to  an  expanding  brake  is  shown  in  Fig.  246,  and  is  identical  in 
principle  with  the  double-armed  lever  contracting  mechanism 
already  described. 


BRAKES.  375 

Details  of  Expanding  Brakes. — The  anchorage  of  expanding 
brakes  is  always  substantially  opposite  the  expanding  mechanism. 
When  both  internal  and  'external  Hub  brakes  are  fitted,  the  same 
brake  support  usually  serves  for  both,  but  if  there  are  only  ex- 
panding hub  brakes,  the  brake  supports  '  lay  be  located  inside 
the  brake  drums  to  reduce  the  overhang,  or  the  segments  may 
even  be  supported  symmetrically.  The  brake  segments  are  made 
either  of  malleable  iron  castings,  drop  forgings  or  band  steel. 
When  they  are  drop  forged  or  cast  they  are  usually  made  of  T- 
section,  while  if  they  are  made  of  band  steel  the  expanding  ends 
are  bent  triangularly  to  form  cam  faces,  or  suitable  lugs  are 
riveted  to  them. 

As  regards  means  for  releasing  the  segments,  they  may  either 
have  a  rigid  hinge  support,  in  which  case  the  friction  facing 
must  not  come  closer  than  about  30  degrees  to  the  point  of 
support,  or  they  may  be  supported  yieldingly  in  the  axial  direc- 
tion, in  which  case  the  friction  material  may  extend  to  the  very 
ends  of  the  segments.  The  first  arrangement  makes  the  simplest 
construction,  as  all  that  is  necessary  to  prevent  dragging  of  the 
segments  when  released  is  to  provide  a  tension  spring  extending 
between  the  two  segments,  preferably  as  close  to  the  ends  as 
possible  without  interfering  with  the  expanding  mechanism. 
With  the  second  arrangement  the  supporting  stud  extends 
through  oblong  holes  in  the  end  of  the  brake  sectors  and  either 
two  or  three  springs  have  to  be  provided  to  insure  clearance 
between  the  segments  and  drum  all  around  when  the  brake  is 
released.  Sometimes  only  a  single  expanding  member  is  used 
(Fig.  244),  forming  almost  a  complete  ring  and  having  an 
anchoring  slot  at  the  middle  of  its  length  into  which  extends  the 
flattened  end  of  the  brake  supporting  arm  or  a  laterally  extend- 
ing stud. 

Expanding  brakes  can  be  calculated  by  the  same  methods  as 
used  for  contracting  band  brakes,  at  least  those  in  which  the 
expanding  force  is  applied  to  the  ends  of  the  segments  in  a 
direction  substantially  tangential  to  their  circumference  at  the 
cut.  The  brake  rods  extending  forward  from  the  brakes  are 
generally  made  either  y%  inch  or  &  inch  in  diameter  in  pleasure 
cars  and  */2  inch  in  trucks. 

Facing  Materials. — In  American  practice  the  segments  of 
expanding  brakes  are  generally  faced  with  asbestos  friction 
fabric.  In  Europe,  on  the  other  hand,  the  expanding  members 
usually  have  metallic  friction  surfaces,  either  cast  iron  or  bronze, 
as  shown  in  the  accompanying  cut  of  the  Panhard  brakes,  Fig. 


376 


BRAKES. 


247.  Cast  iron  on  steel  without  lubrication  has  a  friction  coeffi- 
cient of  about  0.15  which  is  quite  satisfactory.  The  objection- 
able feature  of  metallic  brake  surfaces  is  that  they  lose  very 
much  of  their  effectiveness  when  they  are  covered  with  oil  or 
grease,  and  since  the  brake  drums  are  nearly  always  located  close 
to  some  bearing,  it  is  rather  difficult  to  keep  oil  out  of  them.  It 
will  be  seen  from  Fig.  247  that  in  the  Panhard  brake  the  lining 
strips  are  cut  with  slanting  grooves  designed  to  scrape  the  oil 


/ 


FIG.  247. — PANHARD  BRAKES. 


off  the  brake  drums.  In  order  to  prevent  oil  from  the  rear  axle 
housing  working  out  to  the  brake  drums,  it  is  necessary  to  pro- 
vide packings  at  both  sides  of  the  driving  gear  housing,  and 
there  also  should  be  some  kind  of  oil  guard  at  the  inner  end  of 
the  wheel  hubs.  Asbestos  fabric  possesses  the  two  valuable  fea- 
tures that  its  friction  is  little  affected  by  oil  on  it,  and  that  it  is 
not  spoiled  by  heat.  Grease  cups  must  be  provided  for  all  bear- 
ings of  the  brake  mechanism  and  the  bearings  for  overhanging 
parts  must  be  made  relatively  long. 


BRAKES. 


377 


The  brake  support  is  generally  in  the  form  of  a  malleable 
casting  which  is  riveted  to  the  axle  tube.  Sometimes  this  sup- 
port is  a  full  disc  and  forms  the  cover  for  the  brake  drum,  while 
in  other  designs  it  is  in  the  form  of  a  bracket  or  spider  with 
ribbed  arms,  which  has  a  sheet  metal  disc  fastened  to  it  to  close 
the  brake  drums.  It  is  customary  to  have  the  brake  drum  ex- 
tend over  the  edge  of  the  closing  disc  and  leave  a  clearance  of 
about  3*2  inch  between  the  two  parts. 


FIG.  248.— TIM  KEN  BRAKES. 

The  Timken  internal  and  external  brakes,  illustrated  in  Fig. 
248,  are  good  examples  of  American  brake  design. 

Brake  Adjustment — The  facing  material  of  the  brakes  wears 
in  the  course  of  time  and  this  makes  adjustment  necessary.  With 
some  designs  of  expander  mechanism,  such  as  the  toggle  links, 
adjustment  can  be  made  in  the  length  of  the  ring  formed  by  the 
brake  segments  and  their  connections.  In  the  case  of  other  ex- 
pander mechanisms,  like  the  cam,  the  adjustment  must  be  made 
outside  the  brake  drum.  When  the  brake  lining  is  worn  the 
cam  has  to  be  turned  further  in  order  to  apply  the  segments 
firmly  to  the  drum,  and  if  it  is  found  that  it  cannot  be  turned 


378 


BRAKES. 


sufficiently  far  with  the  original  adjustment  of  the  brake  linkage, 
then  the  lever  on  the  cam  shaft  has  to  be  moved  around  the 
shaft.  A  design  of  adjustable  brake  lever  is  shown  in  Fig.  249. 
The  device  comprises  in  reality  two  levers,  one  free  on  the  shaft 
and  the  other  keyed  to  it.  The  short,  fixed  lever  is  provided 
with  a  slotted  sector  to  which  the  free  lever  can  be  secured  by 
means  of  a  clamp  screw.  The  clamping  surfaces  are  grooved 
to  prevent  slipping. 

Brake  Equalizers — Unless  the  brakes  on  opposite  sides  of  a 
car  produce  equal  retarding  effects  the  car  has  a  tendency  to 
skid.  In  order  to  produce  these  equal  retarding  effects  the  first 
thing  necessary  is  to  apply  equal  operating  forces  to  the  two 


FIG.  249. — BRAKE  LEVER  ADJUSTMENT. 

brakes  of  each  set.  This  necessitates  an  equalizing  device  in  the 
brake  operating  linkage,  which  usually  takes  the  form  of  a  bal- 
ance lever.  A  few  makers,  following  a  design  which  originated 
in  France,  use  a  long  balance  lever  extending  entirely  across 
the  frame,  through  slots  in  the  side  members  or  formed  by 
guides  secured  to  the  under  side  of  the  side  members.  The  bal- 
ance levers  are  made  of  sheet  steel  bent  double,  with  the  width 
decreasing  from  the  middle  toward  the  ends,  and  sometimes  holes 
are  punched  through  the  sheet  metal  to  lighten  the  levers.  (F'g. 
250).  These  balance  levers  are  placed  comparatively  far  to  the 
rear,  about  even  with  the  most  forward  part  of  the  road  wheels, 
so  as  to  make  the  connections  to  the  brakes  outside  the  frame 
short 


379 


FIG.  250. — LONG  BAR  EQUALIZER. 

The  more  common  form  of  brake  equalizer  is  illustrated  in 
Fig.  251.  The  principle  is  the  same  as  that  embodied  in  the 
equalizer  just  described,  but  the  balance  lever  is  much  shorter 
and  the  brake  operating  effort  is  transmitted  to  the  sides  of  the 
frame  by  members  working  under  torsion  instead  of  under  bend- 
ing stresses.  Where  it  is  not  possible  to  support  the  brake  equal- 
izing shafts  by  intermediate  bearings,  the  equalizing  lever  should 


FIG.  251. — CONVENTIONAL  EQUALIZER. 


380 


BRAKES. 


preferably   be  placed  close  to  one  side  of  the  frame,  so  as  to 
minimize  the  bending  moments. 

We  have  so  far  supposed  that  connection  from  the  hub  brakes 
forward  is  made  by  rods  located  outside  the  frame.  These  rods 
tend  to  give  the  chassis  a  "trappy"  appearance,  especially  if  they 
are  long  enough  to  show  in  front  of  the  wheels,  and  many  de- 
signers prefer  to  place  all  rods  inside  the  frame.  This  necessi- 
tates an  extra  pair  of  bearings  for  the  brake  expander  shafts  as 
shown  in  Fig.  252.  Sometimes  these  bearings  are  carried  by 
arms  just  inside  the  springs,  while  in  some  designs  of  rear  axles 
these  extra  bearings  are  close  to  the  driving  gear  housing.  When 
located  in  the  last  described  manner  the  equalizing  lever  may  be 


FlG.  252.— BRAKE  SHAFTS  CARRIED  IN  DOUBLE  BEARINGS. 

connected  directly  to  the  short  levers  at  the  inner  ends  of  the  ex- 
pander snatts. 

Arrangement  of  Brake  Rods— The  forward  connections  of 
the  hub  brake  rods  should  be  so  located  that  the  compression  and 
extension  of  the  rear  springs  will  not  affect  the  application  of 
the  brakes.  This  point  is  of  particular  importance  in  connection 
with  motor  trucks,  on  account  of  the  comparatively  large  motion 
of  the  springs  when  the  truck  is  loaded  or  unloaded,  but  in  the 
past  it  often  has  been  overlooked.  If  a  motor  truck  has  to  be 
stopped  for  loading  or  unloading  on  a  grade,  unless  the  brake 
connections  are  properly  designed,  the  brakes  are  liable  to  loosen 


BRAKES. 


381 


382 


BRAKES. 


BRAKES.  383 

as  the  load  is  put  on,  and  the  truck  will  begin  to  move  down 
hill;  or,  in  the  opposite  case,  the  connecting  linkage  may  be  put 
under  such  tension  by  the  load  as  to  make  it  difficult  to  disengage 
the  brake  lever  after  the  truck  is  loaded. 

As  the  springs  compress  and  distend,  the  rear  axle  and  every 
part  supported  by  it  move  in  circular  paths  around  the  axis  of 
the  forward  radius  rod  connection.  Therefore,  in  order  to  ob- 
viate any  influence  of  spring  action  on  the  application  of  the 
brakes,  the  centre  D  of  the  forward  brake  rod  connection  should 
lie  in  the  axis  of  the  forward  radius  rod  connection.  This,  how- 
ever, is  generally  impossible  in  prajctice.  The  best  practical  solu- 
tion of  the  problem  is  to  place  the  forward  connection  D  of  the 
brake  rod  on  the  line  connecting  the  axis  O  of  the  forward 
radius  rod  connection  with  the  point  P  representing  the  mean 
position  of  the  centre  of  the  rear  brake  rod  connection  with  rela- 
tion to  the  frame,  as  shown  in  Fig.  225.  The  forward  brake  rod 
connection  D  may  be  either  forward  or  to  the  rear  of  the  for- 
ward radius  rod  connection  0,  but  should  be  as  close  to  it  as 
conditions  will  permit.  Fig.  253,  which  is  taken  from  an  article 
by  Edward  L.  Martin  in  THE  HORSELESS  AGE  of  September  4, 
1912,  shows  in  the  sub-figure  that  there  is  still  a  slight  effect  of 
the  spring  action  on  the  brake,  but  with  relatively  long  brake 
rods  it  is  negligible.  When  D  is  located  above  the  line  O  P 
(as  shown  at  D')  the  brakes  tighten  when  the  load  is  removed; 
when  D  is  below  OP,  the  brakes  loosen  when  the  load  is  re- 
moved. 

Front  Wheel  Brakes— Front  wheel  brakes  came  into  vogue 
in  England  in  1909  and  are  still  being  fitted  to  perhaps  a  dozen 
British  and  Continental  cars,  but  there  does  not  appear  to  be  an> 
likelihood  that  they  will  become  universal.  When  such  brakes 
are  used  in  conjunction  with  rear  wheel  brakes,  the  whole  weight 
of  the  car  and  load  is  available  for  braking  purposes,  and  it 
should  be  possible  to  stop  a  car  in  substantially  half  the  distance 
as  with  brakes  on  one  set  of  wheels  only.  The  chief  advantage 
of  front  wheel  over  rear  wheel  brakes  is  that  the  former  do  not 
tend  to  cause  the  car  to  skid.  Another  advantage  claimed  for 
them  is  that  their  use  tends  to  equalize  the  wear  on  front  and 
rear  tires. 

In  this  connection  an  explanation  of  why  the  application  of 
brakes  acting  through  the  rear  wheels  tends  to  cause  the  car 
to  skid  may  be  of  interest.  A  wheel  can  rotate  and  progress 
along  the  road  by  rotation  only  in  its  own  plane,  and  this  plane 
for  the  rear  wheels  is  determined  by  the  motion  of  the  front 


384 


BRAKES. 


wheels,  which  latter  is  controlled  by  the  driver.  Hence,  while 
the  wheels  rotate  they  have  a  directing  tendency,  but  as  soon 
as  they  are  locked  and  begin  to  slide  they  lose  all  directing 
tendency — unless  they  happen  to  be  in  deep  ruts — because  on 
a  hard,  slippery  surface  the  wheels  will  slide  just  as  easily 
sideways  as  in  the  direction  of  their  plane.  Skidding,  of 
course,  occurs  only  when  the  road  surface  is  slippery.  When 
the  brake  is  applied  while  the  car  is  traveling  on  such  roads 
it  takes  very  little  effort  to  lock  the  wheels.  The  car  is  then 
kept  in  motion  by  the  force  of  inertia,  which  acts  at  its  centre 
of  gravity.  This  is  opposed  by  the  resistances  encountered 
by  the  four  wheels  and  it  is,  of  course,  quite  possible  that  the 
resultant  of  these  four  resistance  forces  does  not  pass  through 
the  centre  of  gravity  of  the  car.  We  then  have  a  couple  which 
tends  to  swing  the  car  around,  and  as  the  rear  wheels  will 
slide  as  easily  sideways  as  forwards,  the  smallest  couple  of  this 
kind  will  start  skidding. 


FIG.  255.— SPRAG. 

However,  the  fitting  of  brakes  to  fpont  wheels  involves  many 
mechanical  difficulties  and  none  of  the  designs  that  have  come  to 
the  writers  attention  are  free  from  weak  points.  In  the  first 
place,  the  steering  pivot  axis  produced  must  pass  through  the 
ground  contact  of  the  tires,  as  otherwise  any  difference  in  the 
retarding  action  of  the  two  brakes  will  affect  the  steering.  To 
prevent  such  interference  with  the  steering  either  the  steering 
pivots  may  be  placed  inside  the  hub  of  the  wheel  or  else  the  steer- 
ing pivot  or  both  it  and  the  wheel  may  be  inclined  so  as  to  in- 
sure intersection  of  the  pivot  axis  and  wheel  centre  plane  at  the 
ground  contact. 


BRAKES.  385 

Special  difficulties  are  involved  in  transmitting  the  operating 
motion  to  the  brake  segments,  because  of  the  pivotal  motion  of  the 
brakes.  One  member  of  the  operating  linkage  usually  passes 
through  a  hollow  steering  pivot  pin.  The  manner  in  which  the 
problem  has  been  solved  by  the  designer  of  the  Crossley  car  is 
illustrated  in  Fig.  254.  A  toggle  expanding  mechanism  is  used, 
a  pin  passing  through  the  hollow-inclined  steering  pivot  pin  con- 
necting with  the  toggle  links  through  a  ball  and  socket  joint. 
The  top  end  of  this  operating  pin  is  provided  with  a  flange  and 
surrounded  by  a  return  spring,  and  is  pressed  against  by  the  ball 
ended  arm  of  a  bell  crank  fulcrumed  on  the  steering  fork. 
The  other  arm  of  this  bell  crank  connects  by  a  short  link 
to  a  point  on  the  vehicle  frame. 

It  seems  that  the  torque  on  the  front  axle  produced  by  the  ap- 
plication of  front  wheel  braked  is  always  taken  up  by  the  front 
springs,  no  special  torque  members  being  provided.  Front  wheel 
braking  therefore  imposes  additional  strains  upon  the  axle, 
springs  and  steering  connections,  and  in  most  cars  these  parts 
would  have  to  be  strengthened  if  front  wheel  brakes  were  to  be 
fitted. 

Sprags. — It  has  been  customary  among  European  designers  to 
fit  touring  cars  with  sprags  to  prevent  them  from  running  back- 
ward down  hill.  Owing  to  the  fact  that  the  brakes  now  fitted  are 
entirely  reliable  as  regards  checking  both  forward  and  rearward 
motion,  the  sprag  has  largely  disappeared  from  pleasure  cars,  but 
it  seems  to  become  a  standard  fitment  of  motor  trucks.  This 
may  possibly  be  due  to  the  fact  that  in  many  motor  trucks  the 
rear  wheel  brake  connections  are  so  arranged  that  the  brakes  will 
loosen  either  on  loading  the  truck  or  on  unloading  it.  At  any 
rate,  with  a  heavy  vehicle  which  occasionally  has  to  be  stopped 
and  loaded  or  unloaded  on  very  steep  grades,  it  is  certainly  a 
good  plan  to  have  a  variety  of  stopping  devices. 

The  ordinary  sprag  consists  merely  of  a  straight  steel  rod 
hinged  to  the  axle  or  a  fitting  thereon,  at  its  forward  end,  and 
pointed  or  wedge-shaped  at  its  rear  end,  which  is  designed  to  dig 
into  the  road  surface.  The  sprag  is  generally  formed  with  a 
flange  near  its  lower  end,  to  prevent  it  from  sinking  too  far  into 
the  ground.  Sprags  are  .made  of  such  a  length  that  when  the 
free  end  rests  on  the  ground  their  horizontal  projection  is  equal 
to  1.75 — two  times  its  vertical  projection.  Generally  two  sprags 
are  used,  one  near  each  body  spring. 


CHAPTER  XIV. 


FRONT  AXLES. 

Front  axles  for  pleasure  cars  are  almost  invariably  drop  forged 
from  medium  carbon  steel,  heat  treated.  The  material,  when 
thus  treated,  has  a  tensile  strength  of  90,000  to  100,000  pounds 
per  square  inch  and  may  be  worked  at  10,000  pounds  per  square 
inch.  If  high  tensile  alloy  steel  is  used,  the  stress  may  be  as 
high  as  15,000  pounds  per  square  inch  The  axles  are  always 
of  the  pivoted  type,  the  wheel  spindles  being  made  separate  from 
the  middle  part  of  the  axle  and  connected  with  it  by  a  substan- 
tially vertical  pivot  joint,  thus  forming  so-called  Ackerman 
steering  axles.  A  few  use  tubular  axles  with  drop  forged 
steering  heads  or  axle  ends  secured  to  them.  Pressed  steel 
front  axles  consisting  of  either  a  single  channel  or  two  chan- 
nels fitted  into  each  other  and  having  the  steering  head  riveted 
to  them  are  used  to  some  extent.  Front  axles  for  commer- 
cial vehicles  are  generally  forged  of  medium  carbon  steel,  of 
either  solid  rectangular  section  or  of  I-section  approaching 
a  full  rectangular  section.  Cast  steel  front  axles  are  also  used 
for  commercial  vehicles.  If  the  axle  is  forged  from  medium 
carbon  steel  under  a  steam  hammer  a  stress  of  15,000  pounds 
per  square  inch  can  be  allowed,  but  in  a  cast  steel  axle  the  stress 
should  not  exceed  10,000  pounds  per  square  inch.  Russell  Huff 
(S.  A.  E.  Bulletin,  July,  1916)  found  the  average  factor  of  safety 
in  front  axles,  based  on  the  elastic  limit,  to  be  5.8. 

Stresses  on  Front  Axles— When  the  car  is  at  rest  the  front 
axle  is  subjected  to  bending  moments  in  a  vertical  plane,  due  to 
the  weight  resting  on  the  springs  and  to  its  own  weight.  When 
the  car  is  in  motion  there  is  also  a  horizontal  bending  moment, 
due  to  the  resistance  to  motion  encountered  by  the  front  wheel. 
This  horizontal  moment  is  comparatively  slight  when  the  car  is 
running  on  a  smooth,  level  highway,  but  assumes  considerable 
values  when  the  front  wheel  strikes  an  obstruction.  The  exact 
limiting  value  of  this  horizontal  moment  is  impossible  of  de- 
termination, but  accumulated  experience  has  shown  a  certain 

386 


FRONT  AXLES.  387 

proportion  between  the  vertical  resisting  moment  and  the  hori- 
zontal resisting  moment  of  the  axle  section  to  be  desirable. 

Owing  to  the  small  weight  of  the  axle  itself  as  compared  with 
the  weight  resting  on  the  springs,  the  former  may  be  neglected. 
Of  course,  when  a  new  car  is  being  designed,  the  weight  that 
will  come  on  the  front  axle  is  not  known  in  advance,  but  for 
pleasure  cars  it  may  be  predetermined  with  sufficient  accuracy 
for  the  present  purpose  by  means  of  the  following  equation: 
wheel  base2 

W  =  +  200  pounds. 

10 

In  the  case  of  trucks,  unless  a  similarly  proportioned  vehicle 
on  hand  permits  of  making  a  direct  determination  of  the  dis- 
tribution of  the  weight  between  the  two  axles,  it  may  be  esti- 
mated that  three-eighths  of  the  combined  weight  of  the  truck  and 
load  is  carried  on  the  front  axle,  and  five-eighths  on  the  rear  axle. 
The  approximate  weights  of  commercial  vehicles  are  as  follows : 
Load  capacity  (pounds)  1,500  2,000  3,000  4,000  6,000  10,000 
Chassis  weight  (pounds)  2,400  3,000  3,500  4,500  6,000  8,000 
Body  weight  (pounds).  750  900  1,050  1,200  1,500  1,800 

In  the  great  majority  of  cars  this  weight  is  supported  on  the 
axle  through  the  intermediary  of  two  body  springs,  and  one- 
half  of  it  rests  on  each  spring  saddle.  The  front  axle  itself  is 
supported  at  the  centre  of  the  front  wheel,  and  therefore  forms 
a  simple  beam  with  two  symmetrically  located  loads. 

Front  springs  are  invariably  placed  directly  underneath  the 
frame  side  members  and  this  determines  the  position  of  the 
spring  seats.  The  width  of  the  forward  end  of  the  frame,  in 
turn,  is  determined  by  the  maximum  steering  motion  of  the  front 
wheels  desired.  The  spring  seats  are  generally  forged  integral 
with  the  axle,  though  occasionally  they  are  bolted  on,  in  which 
case  the  axle  is  formed  with  lugs  for  the  bolt  holes.  Between 
spring  seats  practically  all  axles  have  a  downward  curve  or 
drop,  the  object  being  to  insure  proper  clearance  for  the  radiator 
or  whatever  other  part  comes  directly  above  it. 

In  the  conventional  design  of  chassis  the  only  connection  be- 
tween the  front  axle  and  the  frame  is  through  the  front  springs, 
but  a  few  cars  having  unusual  types  of  springs,  such  as  single 
cross  springs  or  coiled  springs,  have  distance  rods  between  the 
front  axle  and  frame  to  transmit  the  driving  thrust  to  the  axle. 
Hence,  neglecting  the  weight  of  the  front  axle  itself,  in  the  con- 
ventional design  all  the  forces  acting  at  the  ground  contact  of 
the  wheels  are  transmitted  to  the  frame  through  the  springs,  the 
horizontal  forces  as  well  as  the  vertical  forces.  The  vertical 


388 


FRONT  AXLES. 


bending  moment  increases  from  nothing  in  the  centre  plane  of 
the  wheel  to  the  maximum  at  the  centre  of  the  spring  seat  and 
remains  at  the  maximum  between  spring  seats.  The  horizontal 
bending  moment,  which  may  attain  considerable  values  when  one 
wheel  strikes  an  obstruction,  increases  from  nothing  in  the  centre 
plane  of  the  wheel  to  a  maximum  at  the  centre  of  the  spring  seat. 
In  the  case  of  an  axle  connected  to  the  frame  by  semi-elliptic 
springs  it  practically  ceases  at  the  spring  seat,  being  taken  up  by 
the  spring.  On  the  other  hand,  in  the  case  of  an  axle  connected 
to  the  frame  by  distance  rods,  the  horizontal  bending  moment  due 
to  forces  on  one  wheel  reaches  its  maximum  at  the  centre  of 
the  spring  seat  and  decreases  to  nothing  at  the  centre  of  the 
other  spring  seat.  In  order  to  give  I-section  axles  the  necessary 
strength  to  withstand  considerable  horizontal  shocks  on  the 
wheels,  it  is  customary  to  gradually  increase  the  width  of  the  top 
flange  from  the  steering  head  toward  the  spring  seat.  In  an  axle 
which  connects  to  the  frame  only  by  semi-elliptic  springs  this 
widening  stops  at  the  spring  seat,  and  that  part  of  the  axle  between 
spring  seats  is  made  of  uniform  section  throughout.  On  the  other 
hand,  in  an  axle  connected  to  the  frame  by  distance  rods  the 
flanges  of  the  axle  should  increase  in  width  as  they  approach  the 
distance  rod  connection  from  both  sides. 

I°Section  Axles  —  The  propor- 
tions of  the  I-section  vary  con- 
siderably in  different  makes  of 
axles,  but  the  section  shown  in 
Fig.  256  is  a  good  average.  De- 
noting the  thickness  of  the  web  by 
a,  the  width  of  the  section  is  6  a 
and  the  height  slightly  over  8  a. 
The  ends  of  the  flanges  are  semi- 
circular, of  radius  a/2,  and  the 
fillet  between  web  and  flange  has 
a  radius  o.  The  sides  of  the 
flanges  are  inclined  7  degrees  to 
give  the  necessary  draught.  The 
dotted  figure  represents  an  equiva- 
lent geometric  section,  and  in 

this  the  height  is  exactly  8  times  the  thickness  of  the  web.  The 
thickness  of  the  flange  of  the  geometric  equivalent  section  is 
f-a.  The  moment  of  inertia  of  such  a  section  is 


FIG.  256. — I-SECTION  OF 
FRONT  AXLE. 


^  I88  a4 


12 


FRONT  AXLES. 


389 


The  distance  c  of  the  outermost  fibre  from  the  neutral  section 
being  4  a,  the  section  modulus  is 


The  moment  of  inertia  of  this  same  section  around  a  vertical 
axis  is 

2X|aX(6«)3  +  5f«Xa3_ia  ,T  „< 

12 

and  since  the  distance  c  in  this  case  is  3  a,  the  horizontal  section 
modulus  is 


of  Action  in  Inches. 
*& 


6OO  TOO  GOO  JOO  /OOP  S1CO 

Mzscimum  Load  in  Pounds  on  Each  £jpringr  Saddle. 

CHART  III  FOR  DETERMINING  FRONT  AXLE  DIMENSIONS. 


J200 


390 


FRONT  AXLES. 


The  section  modulus  is  a  measure  of  the  strength  of  the  section, 
and  the  section  shown  in  Fig.  256  therefore  is  three  times  as 
strong  vertically  as  horizontally. 

Chart  III  permits  of  quickly  determining  the  necessary  section 
of  axle  for  any  load  on  the  spring  pads  and  any  distance  be- 
tween the  centres  of  the  spring  pad  and  wheel  centre.  In  addi- 
tion to  the  section  above  discussed,  another,  somewhat  fuller 
section,  which  was  found  to  be  the  mean  of  a  large  number  of 
American  front  axle  sections  in  1907,  is  also  drawn  in,  and  the 
diagram  also  permits  of  determining  the  necessary  dimensions  of 
this  section  for  various  loads  and  lever  arms.  It  should  be 


FIG.  257.— ELLIOTT  TYPE  STEERING  HEAD  WITH  INTEGRAL  PIVOT 

PINS. 

pointed  out  that  the  diagram  is  based  on  a  unit  stress  of  10,000 
pounds  per  square  inch. 

Steering  Heads. — There  are  three  types  of  steering  heads  now 
in  use,  known,  respectively,  as  the  Elliott,  the  reverse  Elliott  and 
the  Lemoine.  In  American  practice  the  Elliott  type  is  most  ex- 
tensively used  and  the  Lemoine  least.  In  the  Elliott  type  the 
ends  of  the  axle  forging  are  forked  and  the  steering  knuckle  is 
T-shaped;  in  the  reversed  Elliott  type  the  steering  knuckle  is 
forked  and  the  ends  of  the  axle  forms  a  T.  In  the  Lemoine  type 
the  ends  of  the  axle  as  well  as  the  steering  knuckles  form  Ls. 


FRONT  AXLES. 


391 


Elliott  Type— The  spread  of  the  fork  in  Elliott  type  steering 
heads  varies  with  the  moment  of  the  ground  reaction  on  the 
wheels  at  the  centre  of  the  steering  pivot.  The  minimum  dis- 
tance between  the  branches  of  the  fork  is  about  4  inches.  For  a 
moment  of  3,000  Ibs.-ins.  it  can  be  made  4^2  inches,  and  one  inch 
more  for  each  additional  3,000  Ibs.-ins. 

There  are  several  different  designs  of  Elliott  type  steering 
heads  and  knuckles.  In  the  first  place,  the  knuckle  may  either 
be  provided  with  integral  bearing  pins  which  extend  through 
bearing  holes  in  the  fork  arms  of  the  axle,  or  its  vertical  member 


FIG.  258.— ELLIOTT  TYPE  STEERING  HEAD  WITH  PIVOT  PIN  BEAR- 
INGS IN  KNUCKLE. 

may  be  drilled  for  a  steering  pivot  pin.  In  case  the  latter  con- 
struction is  adopted  the  pin  may  have  a  bearing  either  in  the 
fork  ends  or  in  the  vertical  member  of  tne  knuckle.  A  design 
of  steering  knuckle  with  integral  bearing  pins  is  illustrated  in 
Fig.  257.  The  lower  arm  of  the  fork  has  a  hole  Grilled  through 
it  larger  in  diameter  than  the  vertical  member  of  the  knuckle. 
The  bearing  pin  at  the  lower  end  of  the  knuckle  is  considerably 
smaller  in  diameter  than  this  hole,  and  the  remaining  space  is 
taken  up  by  a  bearing  bushing  screwed  into  the  hole  and  locked 
in  place.  In  this  particular  design  of  front  axle  the  vertical  load 
is  transmitted  from  the  axle  to  the  knuckle  through  a  single  steel 


392 


FRONT  AXLES. 


ball  of  large  diameter,  which  rests  in  the  end  of  the  drill  hole  in 
the  upper  arm  of  the  steering  fork  and  on  a  spherical  depressior- 
on  top  of  the  vertical  member  of  the  knuckle.  The  steering  arm 
in  this  case  is  bolted  right  through  the  vertical  member  of  the 
knuckle.  It  can  easily  be  seen  that  the  entire  vertical  load  is 
taken  by  the  upper  arm  of  the  fork,  and  the  latter  must  be  pro- 
portioned accordingly. 

A  design  of  steering  knuckle  in  which  a  pivot  pin  passes 
through  the  vertical  member  of  the  knuckle  is  shown  in  Fig.  258. 
The  pin  has  its  bearings  in  the  knuckle  and  is  a  tight  fit  in  the  fork 


FIG.  259. — ELLIOTT  TYPE  STEERING  HEAD  WITH  BEARINGS  IN 
STEERING  FORK. 

arms.  The  pivot  bolt  is  bolted  into  the  lower  arm  of  the  fork, 
being  shouldered  and  provided  with  a  castellated  nut  at  the  bot- 
tom, and  is  drilled  for  a  small  grease  cup.  Bearing  bushings  are 
inserted  into  the  vertical  member  of  the  knttckle  from  each  end, 
and  at  the  top  there  is  a  ball  thrust  bearing  for  carrying  the 
weight.  The  steering  arm  is  bolted  into  a  lug  on  the  lower  end 
of  the  vertical  member. 

A  third  design  in  which  the  bearings  for  the  pivot  pin  are  in 
the  fork  arms  is  shown  in  Fig.  259. 

Other  Types.— Fig.  260  illustrates  the  reversed  Elliott  type  of 
steering  head  and  knuckle,  which  type  was  introduced  by  the 
German  Daimler  Co.,  and  is  used  most  extensively  on  foreign 


FRONT  AXLES. 


393 


cars.  The  bearings  are  always  in  the  knuckle  fork,  and  are  pro- 
vided with  hardened  steel  bushings.  A  ball  thrust  bearing  may 
be  fitted  as  shown,  but  the  majority  of  steering  heads  of  this 
type  have  plain  thrust  bearings,  notwithstanding  the  fact  that  they 
are  used  particularly  on  high  grade  cars.  With  a  reverse  Elliott 
steering  head  the  distance  from  the  centre  of  the  wheel  to  the 
centre  line  of  the  pivot  is  necessarily  somewhat  larger  than  with 
other  types,  and  a  ball  thrust  bearing  tends  to  further  increase 
this  distance,  which  is  probably  the  reason  it  is  generally  dis- 
pensed with.  This  difficulty  is  neatly  overcome  in  several  Eng- 
lish cars.  The  pivot  pin  is  enlarged  at  the  lower  bearing,  so 
as  to  form  a  shoulder  which  bears  against  the  under  surface  of 


FIG.  260. — REVERSED  ELLIOTT  TYPE  STEERING  HEAD. 

the  steering  head,  and  the  ball  thrust  bearing  surrounds  the.  pin 
on  top  of  the  steering  knuckle,  being  held  in  place  by  means  of  a 
castellated  nut  on  the  pin.  The  whole  is  surmounted  by  a  sheet 
metal  cap.  In  this  construction,  therefore,  the  end  thrust  is 
transmitted  through  the  pivot  pin. 

In  order  to  make  the  distance  between  wheel  centre  and  pivot 
axis  as  small  as  possible,  the  vertical  part  of  the  fork  is  generally 
made  of  such  a  cross  section  as  to  partly  envelop  the  steering 
head.  The  height  of  the  steering  head  with  the  reverse  Elliott 
type  of  axle  is  generally  little  greater  than  the  height  of  the  axle 
section.  This  is  considerably  less  than  the  spread  of  the  fork  in 
a  corresponding  Elliott  type  axle.  But  the  pivot  pin  diameter  and 
the  length  of  the  bearings  are  made  correspondingly  larger  in 
the  former. 


394 


FRONT  AXLES. 


The  Lemoine  type  of  steering  head  was  formerly  much  used 
in  France,  but  is  now  rarely  met  with.  Fig.  261  illustrates  the 
Winton  steering  head,  which  is  of  this  type.  In  this  particular  de- 
sign the  thrust  load  and  part  of  the  radial  load  on  the  bearing 
are  taken  up  on  a  tapered  roller  bearing,  the  remaining  radial 
load  being  taken  up  on  a  conical  bearing.  In  all  steering  knuckles 
a  liberal  fillet  should  be  provided  where  the  wheel  spindle  joins 
the  vertical  member.  As  ball  and  roller  bearings  have  only  a 
slight  chamfer  a  washer  is  sometimes  placed  between  the  shoulder 
on  the  spindle  and  the  bearing. 

Calculations  of  Pivot  Bearings — In  the  illustrations,  Figs.  257 


FIG.  261.— LEMOINE  TYPE  OF  STEERING  HEAD  (WINTON). 

to  261,  various  methods  for  taking  up  the  thrust  load  are  shown. 
This  thrust  load  is  relatively  large,  equal  to  the  weight  carried 
by  one  wheel  when  the  car  is  at  rest  or  running  over  a  smooth 
road  surface,  and  is  increased  by  shocks  on  uneven  pavement. 
The  simplest  plan  consists  in  providing  two  hardened  steel 
thrust  washers  between  the  vertical  member  of  the  steering 
knuckle  and  the  steering  head.  One  washer  must  be  secured  by 
a  pin  to  the  knuckle  and  the  other  to  the  steering  head,  so  that 
the  motion  will  take  place  between  the  two  hardened  surfaces 
and  not  between  one  hardened  and  one  soft  surface.  The  bear- 
ing surface  of  the  thrust  washers  should  be  made  about  one 
square  inch  per  400  pounds  load.  In  case  a  ball  thrust  bearing 


FRONT  AXLES. 


395 


is  used  its  rated  load  capacity  should  preferably  be  50  per  cent. 
greater  than  the  maximum  load  on  each  front  wheel,  though  con- 
siderations of  space  limitation  often  compel  the  use  of  smaller 
bearings. 

The  load  on  the  radial  bearings  of  the  steering  pivot  may  be 
calculated  as  follows  (Fig.  262)  :  Let  P  represent  the  maximum 
reaction  of  the  wheel  on  the  knuckle  spindle  ;  a  the  distance  from 
the  centre  plane  of  the  wheel  to  the  axis  of  the  pivot;  /  the  dis- 
tance between  centres  of  radial  bearings,  and  P'  the  load  on  each 
radial  bearing. 
Then 


and 


J 

c^ 

r       i 

P 

*     n 

There  is,  however,  still  another  load  on  the  radial  bearings  of  the 
pivot;  namely,  that  due 
to  the  resistance  to  mo- 
tion encountered  by  the 
front  wheel.  The  resist- 
ance may  attain  quite 
high  values  when  the 
front  wheel  strikes  a 
large  obstruction  while 
the  car  is  going  at  con- 
siderable speed,  but  the 
resulting  bearing  pres-  FlG-  262.— DIAGRAM  FOR  CALCULATING 
sure  lasts  only  for  a  STEERING  PIVOT  LOADS. 

moment  and,  therefore,  need  not  be  considered  in  determining 
the  necessary  bearing  surface.  The  resistance  to  motion  on 
smooth,  hard,  level  roads  throws  a  load  on  the  pivot  which 
is  absolutely  negligible  in  comparison  with  that  due  to  the 
weight  on  the  wheel.  The  radial  bearings  can  be  so  proportioned 
that  the  unit  bearing  pressure  is  about  500  pounds  per  square 
inch.  Usually  the  length  of  the  bearings  is  about  1.5  times  the 
diameter  d.  If  this  relation  holds,  then 

.  P'  _  P         a 
500        500  *   / 
Hence 


/" 


750 


(62) 


If  this  diameter  is  chosen  for  the  pin,  the  latter  will  be  strong 
enough  to  resist  the  shearing  stress  to  which  it  is  subjected. 


396 


FRONT  AXLES. 


The  pivot  axis  is  sometimes  inclined  in  the  vertical  plane 
through  the  centre  of  the  front  axle,  in  order  to  bring  the  point 
of  its  intersection  with  the  ground  closer  to  the  centre  of  wheel 
contact  on  the  ground.  This  distance  forms  the  lever  arm  at  the 
end  of  which  the  resistance  to  motion  of  the  front  wheels  acts 
when  the  driver  attempts  to  swing  them  around  for  steering. 
The  shorter  this  lever  arm  the  easier  the  car  will  be  to  steer, 
and  some  manufacturers  incline  the  spindle  so  much  that  its  axis 
produced  meets  the  ground  at  the  centre  of  wheel  contact,  in 
which  case  the  length  of  the  lever  arm  is  nil  (Fig.  263).  How- 


FIG.    263.— INCLINED    STEERING      FIG.  264.— FORE  AND  AFT  IN- 
PIVOT.  CLINED  STEERING  PIVOT  PRO- 

DUCING TRAILER  EFFECT. 

ever,  this  construction  has  the  disadvantage  that  in  any  but  the 
straight-ahead  position  the  front  wheels  are  considerably  inclined, 
in  which  position  they  are  not  as  strong  with  respect  to  vertical 
loads  as  when  standing  vertically. 

Some  manufacturers  also  incline  the  axles  and  steering  pivots 
in  a  vertical  fore-and-aft  plane  (Fig.  264).     There  are  two  rea- 


FRONT  AXLES. 


397 


sons  for  this  practice.  The  first  is  that  the  combined  load  due  to 
the  weight  on  the  axle  and  the  road  resistance  encountered  by 
the  wheel  is  in  a  slightly  inclined  direction,  and  in  the  case  of 
an  I-section  axle,  of  course,  there  is  an  advantage  in  making  the 
plane  of  maximum  strength  of  the  axle  coincide  with  the  direction  of 
the  load.  The  other  reason — and  probably  the  more  important  one — 
is  that  this  construction  produces  a  trailer  effect  and  tends  to 
obviate  serious  consequences  in  the  event  of  breakage  or  dis- 
connection of  the  steering  linkage.  This  effect  is  similar  to  that 
obtained  with  the  front  wheel  of  a  bicycle,  whereby  a  cyclist  is 
enabled  to  ride  with  his  hands  off  the  handle  bar.  The  point 
of  wheel  contact  with  the  ground  is  located  to  the  rear  of  the 
point  at  which  the  steering  spindle  axis  produced  meets  the 
ground,  hence  the  steering  wheels  trail  and  are  automatically  kept 
in  the  straight  ahead  position  by  the  road  resistance.  The  same 
effect  can  also  be  obtained  by  placing  the  axis  of  the  knuckle 


\\-i-- 

Ml 

i 
—  r 



//   1 

FIG.  265.— STEERING  KNUCKLE  WITH   SPINDLE   SET  BACK  FROM 
PIVOT  Axis. 

spindle  slightly  to  the  rear  of  the  pivot  axis,  as  shown  in  Fig. 
265.  This  latter  arrangement  has  been  used  to  quite  an  extent 
in  France  in  connection  with  built-up  knuckles,  the  wheel  spindle 
being  bolted  to  the  vertical  member  of  the  knuckle. 

Front  Wheel  Bearings — All  of  the  different  types  of  anti- 
friction bearings  are  used  in  front  wheels.  There  is  considerable 
end  thrust  on  the  front  wheel  bearings,  and  in  case  radial  ball 
or  parallel  type  roller  bearings  are  used,  separate  thrust  bearings 
for  thrusts  in  both  directions  should  preferably  be  fitted,  at  least 
on  heavy  vehicles.  It  is  not  always  fully  realized  that  there  are 
heavy  thrusts  on  front  wheel  bearings.  Rear  axles  are  often 
without  any  thrust  bearings  except  the  one  designed  to  take  up 
the  thrust  of  the  bevel  gear,  and  from  this  it  is  sometimes 
erroneously  inferred  that  there  is  no  need  for  thrust  bearings  in 
the  front  wheels  either.  The  difference  is  that  whereas  the  pro- 
pelling effort  is  always  parallel  to  the  planes  of  the  rear  wheels, 


398  FRONT  AXLES. 

in  turning  a  corner  it  may  make  an  angle  of  30  to  40  degrees 
with  the  planes  of  the  front  wheels.  The  radial  load  on  the 
bearing  due  to  the  force  of  propulsion  is  proportional  to  the 
cosine  of  the  angle  between  the  direction  of  the  propelling  force 
and  the  plane  of  the  wheel,  and  the  thrust  load  is  proportional 
to  the  sine  of  this  angle.  Therefore,  if  the  wheel  stands  at  an 
angle  of  45  degrees,  the  thrust  load  due  to  the  propelling  force 
is  equal  to  the  radial  load  due  to  that  force.  A  factor  tending 
to  aggravate  the  case  with  respect  to  thrust  load  is  that  when 
rounding  a  curve  at  considerable  speed  the  centrifugal  force 
throws  nearly  all  of  the  weight  of  the  car  on  the  outer  wheels, 
and  the  propelling  force  on  the  outer  forward  wheel  is  increased 
in  the  proportion  of  the  weight  on  it.  The  thrust  load  being  pro- 
portional to  the  propelling  force,  it  is  also  increased  by  this  effect. 
There  is,  moreover,  a  thrust  load  on  the  front  wheel  bearings 
due  to  the  centrifugal  force.  In  fact,  this  whole  force  acts  as  a 
thrust  load,  since  it  acts  in  the  direction  of  the  turning  radius 
and  the  axes  of  all  the  wheel  spindles  theoretically  constitute 
radii  of  the  turning  circle.  On  a  smooth,  hard,  level  surface  the 
end  thrust  on  the  wheel  bearings  is  limited  by  the  adherence  of 
the  wheels  to  the  ground,  which  is  about  0.6  of  the  weight  upon 
them  on  most  kinds  of  pavement.  So  far  as  the  end  thrust  due 
to  centrifugal  force  is  concerned,  it  is  the  same  for  the  front 
and  rear  wheel  bearings,  for  unit  weight  upon  them,  but  the  front 
wheel  bearings  in  addition  are  subjected  to  end  thrust  due  to  the 
propelling  force,  from  which  the  rear  wheel  bearings  are  free. 
Thrust  Loads — The  usual  formula  for  centrifugal  force  is 

F=  1.226  wn2r 

where  w  is  the  weight  in  pounds,  «  the  number  of  revolutions  per 
second  and  r  the  radius  in  feet.  If  the  speed  v  is  expressed  in 
miles  per  hour  the  car  makes 

5'2  °v  feet  per  second. 
3,600 

and  the  circumference  of  the  circle  being  2  ^  r  feet,  the  car  will 
turn  at  the  rate  of 

revolutions  per  second. 


5,280    v       0.2334^ 
3,600 

Substituting  this  value  for  n  in  the  expression  for  centrifugal 
force  we  get 

o.o668tvv2.  t*~\ 


FRONT  AXLES.  399 

We  will  assume  a  car  weighing  with  passengers  3,000  pounds, 
whose  centre  of  gravity  is  24  inches  high,  rounding  a  corner  at 
a  radius  of  60  feet.  The  centrifugal  force  necessary  to  overturn 
this  car,  with  a  tread  of  56  inches,  would  be 

3,000  X  -^—  •  =  3,500  founds 
To  find  the  speed  at  which  the  car  would  turn  over  we  put 


o.  0668  X  3,ooo  X*8  = 
60 


-=/ 


_  7     ^      ;     - 


3,000X0.0686 

Of  course  the  car  would  turn  over  only  if  the  ground  ad- 
herence was  sufficient  to  prevent  skidding.  We  will  now  suppose 
that  the  car  turns  the  corner  at  about  half  this  speed,  say  15 
m.  p.  h.  Also,  that  the  weight  resting  on  the  front  wheels  is 
1,200  pounds.  Then  the  centrifugal  force  on  this  weight  will  be 

0.0668  Xi.«ooX  15X15  =  300  tounds  . 

60 

The  centrifugal  force  of  300  pounds  acting  at  the  centre  of 
gravity  will  have  the  effect  of  removing 

300X24  =  I28  founds. 

56 

from  the  inner  wheel  and  adding  it  to  that  on  the  outer  wheel, 
thus  making  the  weight  distribution  472  pounds  on  the  inner 
wheel,  and  728  pounds  on  the  outer.  The  resistance  to  motion 
of  the  outer  wheel  will  thus  be  increased  in  the  ratio  of  728  to 
600.  Furthermore,  the  propelling  effort  applied  to  the  front 
wheels  acts  at  an  angle  whose  sine  is  approximately  1-6,  assum- 
ing that  the  car  has  a  wheel  base  of  10  feet,  and  the  thrust  load 
on  the  bearings  is  one-sixth  of  the  propelling  force. 

It  is  impossible  to  make  a  close  calculation  of  the  thrust  on 
the  front  wheel  bearings  under  any  given  conditions,  because  of 
the  effect  of  the  road  surface  and  the  uncertain  distribution  of 
the  thrust  between  the  inner  and  outer  wheel  bearings,  but  the 
point  to  be  remembered  is  that  whenever  the  car  describes  a 
curve  there  is  end  thrust  on  the  front  wheel  bearings,  even  with 
the  power  shut  off,  because  of  the  centrifugal  force  ;  if  the  motor 
is  propelling  the  car  there  is  additional  end  thrust,  owing  to  the 
oblique  application  of  the  propelling  force  to  the  front  wheels. 

Mounting  of  Bearings  —  Because  of  the  simple  construction, 
combined  radial  and  thrust  bearings  are  much  used  for  front 
wheels,  such  as  Timken  roller,  New  Departure,  cup  and  cone, 


400 


FRONT  AXLES. 


etc.  The  mounting  of  such  bearings  presents  no  particular  diffi- 
culty. If  they  are  of  the  adjustable  type  the  bearings  are  ar- 
ranged with  their  outer  races  pressing  endwise  against  internal 
flanges  on  the  hub  between  a  shoulder  and  a  nut  on  the  knuckle 
spindle,  as  shown  in  Fig.  266.  The  adjusting  nut,  of  course,  must 
be  properly  locked.  Lubricant  is  retained  within  the  hub  by  the 
hub  cap  at  the  outer  end  and  a  dust  washer  on  the  inner  end. 
The  bearings  are  usually  so  placed  that  from  two-thirds  to  three- 
quarters  of  the  load  comes  on  the  inside  one,  though  there  is 
considerable  variation  in  this  respect.  Of  course,  the  aim  always 
is  to  bring  the  centre  plane  of  the  wheel  as  close  to  the  pivot 

axis  as  possible.  A 
clearance  of  about  one- 
quarter  inch  should  be 
allowed  between  the 
vertical  member  of  the 
knuckle  or  the  steering 
head  and  the  nearest 
part  of  the  wheel  hub. 

The  outer  bearing 
serves  mainly  as  a 
steadying  bearing  and 
must  be  placed  at  a  con- 
siderable distance  from 
the  inner  one  to  prop- 
erly serve  its  purpose. 
Adjustable  roller  bear- 
ings on  pleasure  car 
axles  are  placed  at  3  to 
Zl/2  inch  centre  distance, 
while  ball  bearings  are 
placed  at  4  to  5  inch 


FIG.      266. — MOUNTING      OF      FRONT 
WHEEL    ADJUSTABLE    BEARINGS. 


centre  distance.  For  oiling,  a  spring  closed  oil  cup  is  usually 
placed  on  the  hub.  A  much  used  method  of  introducing  lubricant 
into  the  front  hubs  consists  in  removing  the  hub  caps,  filling 
them  with  grease  and  replacing  them. 

There  are  many  light  cars  in  use  employing  only  two  radial 
ball  bearings  in  the  front  wheels.  Where  radial  bearings  only 
are  used,  both  races  of  one  kind  should  be  firmly  secured  againsl 
endwise  motion,  as  well  as  one  race  of  the  other  kind,  the  re- 
maining race  being  left  free  endwise.  Some  designers  clamp 
the  two  inner  races  tight  on  the  spindle  and  place  the  inner  faces 
of  the  outer  races  against  internal  flanges  of  the  hub.  With  this 


FRONT  AXLES. 


401 


construction,  if  the  distance  between  the  outer  faces  of  the  two 
flanges  and  the  length  of  the  spacer  between  the  inner  races  are 
different,  a  permanent  side  thrust  is  put  on  the  bearings,  which 
causes  them  to  work  hard. 

A  neat  mounting  of  radial  and  thrust  bearings  for  front  wheel 
hubs,  due  to  F.  G.  Barrett,  of  England,  is  illustrated  in  Fig.  267. 
In  this  design  the  two  outer  races  of  the  radial  bearings  are 
clamped  in  the  hub,  as  is  the  middle  race  of  the  thrust  bearing. 
Both  inner  races  of  the  radial  bearings  are  free.  The  two  thrust 
bearings  are  assembled  on  a  sleeve  which  fits  closely  over  the 


FIG.  267.— MOUNTING  OF  FRONT  WHEEL  RADIAL  AND  THRUST  BALL 
BEARINGS 


tapered  portion  of  the  knuckle  spindle  and  is  held  in  place  by 
the  nut  on  the  end  of  the  spindle. 

A  good  solution  of  the  front  wheel  bearing  problem  seems  to 
consist  in  the  use  of  a  radial  bearing  at  the  outer  end  and  a  so- 
called  two  row  bearing,  designed  to  take  both  radial  and  thrust 
loads,  at  the  inner  end.  Both  inner  races  are  then  secured  end- 
wise, while  the  outer  race  of  the  radial  bearing  is  left  free  end- 
wise. 

Steering  Spindle  "Set" — The  spindle  of  a  steering  knuckle 
is  arranged  to  make  a  slight  angle  with  the  horizontal,  chiefly  to 


402 


FRONT  AXLES. 


allow  for  flexure  of  the  axle  and  play  in  the  knuckle  joints  when 
the  axle  is  under  load.  In  American  practice  it  is  common  to 
have  the  knuckle  spindle  make  an  angle  of  about  two  degrees  v/ith 
the  horizontal,  if  plane  wheels  are  to  be  used.  If  dished  wheels 
are  to  be  used  the  angle  may  be  as  much  as  6  degrees. 

Spindle  Diameter — As  regards  the  diameter  of  the  knuckle 
spindle,  this  is  generally  determined  by  the  bore  of  the  bearings ; 
that  is  to  say,  if  the  bearings  are  large  enough  to  withstand  the 
load  upon  them,  a  spindle  fitting  their  bore  will  easily  withstand 
the  bending  moments  on  it.  When  radial  ball  bearings  are  used 
the  medium  series  is  usually  selected.  Russell  Huff,  whose  paper 
on  factors  of  safety  was  referred  to  in  the  foregoing,  found  the 


FIG.  268.— STEERING  MOTION  STOPS. 


average  factor  of  Safety  in  the  steering  spindles  at  the  bearing 
shoulder  to  be  26.1. 

Steering  Stops — A  little  refinement  that  has  been  applied  in 
a  number  of  axles  in  recent  years  is  a  stop  limiting  the  swing  of 
the  steering  knuckles,  so  as  to  prevent  contact  between  the  re- 
volving wheel  and  the  frame  or  the  steering  drag  link,  which  is 
objectionable.  Such  a  stop  (L)  is  most  easily  provided  in  the 
case  of  a  reversed  Elliott  type  steering  gear,  as  shown  in  Fig.  268 
at  A.  At  B  in  the  same  figure  is  shown  the  arrangement  used  in 
the  axles  of  the  Timken-Detroit  Axle  Co.,  which  have  Elliott 
type  steering  heads.  In  this  case  a  lug  L  on  the  knuckle  arm  con- 
tacting with  an  adjustable  stop  on  the  axle  forging  limits  the 
steering  motion. 


FRONT  AXLES. 


403 


Knuckle  Arms — The  steering  knuckles  are  provided  with 
arms  for  interconnection  of  the  two  knuckles  on  opposite  sides 
of  the  car  by  the  tie  rod  and  also  for  connection  to  the  steering 
gear  through  the  drag  link.  Of  course  only  one  of  the  knuckles 
needs  to  be  connected  to  the  steering  gear,  and  usually  the  arm 
of  this  knuckle  is  made  double,  though  occasionally,  especially 
with  reversed  Elliott  type  steering  heads,  one  knuckle  is  provided 
with  two  separate  arms.  The  necessary  length  of  the  arms  and 
other  details  will  be  considered  in  the  chapter  on  the  steering 
gear.  It  is  usually  necessary  to  bend  these  arms  out  of  the 


FIG.  269.— DOUBLE  STEERING  ARMS  FOR  ELLIOTT  TYPE  FRONT  AXLE. 

horizontal  plane,  at  least  with  Elliott  type  steering  heads,  because 
the  tie  bar  has  to  pass  underneath  the  body  springs  and  the  drag 
link  must  pass  either  over  or  under  the  axle.  Moreover,  the  arm 
for  connection  to  the  drag  link  must  be  given  a  considerable  curve 
in  the  horizontal  plane,  because  with  the  front  wheel  in  the  central 
or  straight  ahead  position  this  arm  usually  extends  practically 
in  the  direction  of  the  axle,  hence  in  an  Elliott  type  axle  it  must 
curve  around  the  vertical  part  of  the  steering  head  and  it  must 
clear  this  part  for  any  position  of  the  front  wheels.  Knuckle 
arms  are  secured  to  steering  knuckles  with  a  tapered  seat,  being 


404 


FRONT  AXLES. 


bolted  and  keyed.  The  taper  is  made  about  1:10,  and  the  nut  is 
secured  by  means  of  a  cotter  pin.  The  key  is  necessary  because 
of  the  crank  effect  due  to  the  bend  in  the  arm.  As  regards  the 
proper  size  of  the  arm,  let  W  represent  the  maximum  weight  on 
one  front  wheel;  a  the  distance  between  the  pivot  axis  and 
the  centre  plane  of  the  wheel,  and  b  the  distance  between  the  pivot 


FIG.  270. — STEERING  ARMS  FOR  REVERSE  ELLIOTT  TYPE  FRONT  AXLE. 

axis  and  the  axis  of  the  tapered  portion  of  the  knuckle  arm ;  then 
the  diameter  d  of  the  larger  end  of  the  taper  should  be 


/ 
r     i, 


Wa    for  pleasure  cars 


and 


d 


*/  Wa 

=v  ^ 


trucks' 


5006 


The  arm  proper  is  generally  made  of  oval  section,  of  such  size 
as  to  have  the  same  maximum  section  modulus  as  the  tapered 


FRONT  AXLES.  405 

portion  near  the  latter,  and  tapering  down  slightly  toward  the  free 
end.  Fig.  269  shows  two  typical  designs  of  knuckle  arms,  the  one 
on  the  left  being  for  axles  in  which  the  tie  rod  is  located  to  the 
rear,  in  which  case  the  knuckle  arm  must  point  away  from  the 
wheel,  while  the  one  on  the  right  is  for  axles  in  which  the  tie  rod 
is  in  front,  in  which  case  the  arm  must  approach  the  wheel. 
Fig.  270  shows  a  knuckle  arm  designed  for  a  reversed  Elliott 
type  of  knuckle.  One  of  the  advantages  of  this  type  of  steering 
head  is  that  it  interferes  less  with  the  arrangement  of  the 
knuckle  arm. 

It  is  a  good  plan  to  provide  the  knuckle  arm  on  the  driver's 
side  with  a  drilled  boss  for  the  speedometer  gear  bracket,  so  as 
to  make  a  rigid  mounting  of  this  bracket  possible.  The  location 
of  the  holes  is  not  a  matter  of  great  importance,  for  the  reason 
that  universally  adjustable  mountings  for  the  driven  gear  have 
to  be  provided  in  any  case.  A  drilled  boss  permits  of  rigidly 
fastening  the  bearing  bracket  in  place  so  there  is  no  danger  of 
its  being  jarred  loose  and  the  mesh  of  the  gears  becoming  dis- 
turbed. 

Tie  Rod — The  rod  which  connects  the  steering  knuckles  on 
opposite  sides  of  the  car  is  practically  always  made  tubular.  It 
may  be  placed  either  in  front  of  the  axle  or  to  the  rear  of  it. 
The  former  arrangement  has  the  advantage  that  the  rod  ordinarily 
works  under  tension,  while  with  the  latter  it  works  under  com- 
pression. That  is  to  say,  the  road  resistance  encountered  by  the 
front  wheels,  acting  through  the  bell  cranks  formed  by  the  steer- 
ing knuckles  and  arms,  puts  a  tension  on  the  tie  rod  with  the  first 
mentioned  construction  and  a  compression  with  the  second.  Of 
course,  the  force  impressed  upon  the  rod  by  the  driver  in  steering 
the  car  produces  a  tension  for  one  direction  of  motion  and  a 
compression  for  the  other  with  both  constructions.  The  advantage 
claimed  for  the  second  arrangement  is  that  the  relatively  frail  tie 
rod  is  much  better  protected  from  injury  back  of  the  axle  than  in 
front  of  it.  The  great  majority  of  all  cars  now  have  the  tie  rod 
back  of  the  front  axle. 

Considering  the  tie  rod  located  back  of  the  axle,  the  maximum 
compressive  load  may  be  represented  by  the  expression 

p_cWa 
~~b~ 

where  c  is  a  constant;  W,  the  maximum  weight  on  one  front 
wheel ;  a,  the  distance  between  the  centre  plane  of  the  wheel  and 
the  pivot  axis,  and  b,  the  length  of  the  knuckle  arm.  The  rod 


406  FRONT  AXLES. 

acts   like   a   column   with    free    ends,   the   permissible  'load    for 
which  is 

SA 
P  =  Tz 


(Rankin's  equation),  where  S  is  the  safe  working  stress  of  the 
material;  A,  the  sectional  area  of  the  rod;  qt  a  constant;  /,  the 
length  of  the  rod,  and  r  the  least  radius  of  gyration  of  the  sec- 
tion. For  a  solid  rod, 

Z)2 


r"  = 

16 


for  a  tube, 


16 
Hence 

cWa  S  A 


With  the  proportions  obtaining  in  steering  tie  rods  we  may 
write 

c  W  a         SA 
b  /2 

<?r-T 

without  committing  a  great  error.    Remembering  that  for  a  hol- 
low circular  section 

A=--  ^L(D*—d2* 

4 
and 


we  get,  by  substitution, 

cWa 

b  64  ?/ 

which  may  be  transformed  to  read 


All  of  the  factors  in  the  first  pair  of  parentheses  may  be  re- 
garded as  constant,  and  we  may  denote  this  term  by  (7,  which 
gives  us 


Cb 


FRONT  AXLES.  407 

The  value  of  C  should  be  1,000,000  for  pleasure  car  axles  with 
the  tie  rod  in  the  rear;  1,500,000  for  pleasure  car  axles  with  the 
tie  rod  in  front  and  for  truck  axles  with  the  tie  rod  in  the  rear, 
and  2,000,000  for  truck  axles  with  the  tie  rod  in  front.  It  might 
be  argued  that  the  above  reasoning  does  not  apply  to  the  case 
of  a  tie  rod  in  front  of  the  axle,  because  in  the  latter  it  is  nor- 
mally under  tension  instead  of  under  compression.  However, 
it  is  the  extreme  conditions  that  determine  the  necessary  s.^ength 
of  a  part,  and  it  is  most  likely  that  a  tie  rod  in  front  of  the  axle 
is  subjected  to  the  greatest  unit  stress  when  the  driver  suddenly 
wrenches  his  steering  wheel  around  in  such  a  direction  as  to 
put  the  tie  rod  under  compression,  in  case  the  "off"  wheel  is 
restrained  from  turning  in  that  direction  by  a  rut,  etc.  In 
using  equation  (64),  calculate  the  value  of  the  right  hand  term; 
assume  a  value  for  D,  and  calculate  the  necessary  value  of  d. 
If  the  result  is  unsatisfactory  assume  another  value  for  D.  The 
wall  thickness  must  not  be  chosen  too  small,  because  the  tube 
has  to  be  threaded  for  the  connector.  Equation  (64)  is  intended 
for  straight  tie  rods  only;  if  the  rod  is  cranked  at  the  middle 
to  clear  the  engine  or  under-pan  it  must  be  made  stiffen 

The  length  of  the  tie  rod  is  so  adjusted  that  when  the  car 
stands  on  the  factory  floor  with  the  front  wheels  in  the  central 
position,  the  distance  apart  of  the  wheel  rims  in  front  of  the 
axle  at  the  height  of  the  spindle  is  from  %  to  y*  inch  less  than 
the  corresponding  distance  back  of  the  axle.  This  slight  "toeing 
in"  is  intended  to  allow  for  the  slight  play  in  the  joints  and 
flexure  of  the  members  when  the  car  is  being  driven  on  the  road, 
so  that  in  actual  road  driving  the  wheels  will  be  substantially 
parallel. 

Tie  Rod  Connectors— The  ends  of  the  knuckle  arms  swing 
in  the  same  plane,  and  the  tie  rod,  therefore,  is  connected  to 
the  arms  by  forked  connectors.  The  connector  (Fig.  271)  is 
usually  screwed  over  the  end  of  the  tie  rod,  its  hub  being  split 
for  some  distance  along  its  length  and  provided  with  clamp  lugs, 
and  it  is  securely  clamped  down  on  the  rod.  The  bearing  of  the 
connector  pin  may  either  be  in  the  knuckle  arm  or  in  the  con- 
nector. In  high  grade  cars  this  bearing  is  bushed  with  bronze  or 
hardened  steel,  and  lubricating  means  are  provided,  either  a  small 
oil  cup  or,  preferably,  a  small  compression  grease  cup.  The  pro- 
jected bearing  area  should  be  about 

W  a 
A  =  —  —  square  inches. 


408 


FRONT  AXLES. 


Making  the  length  of  the  bearing  from  two  to  three  times  the 
diameter  gives  a  pin  amply  strong  to  withstand  the  shearing 
stress.  Owing  to  the  fact  that  the  safety  of  the  passengers  de- 
pends upon  the  integrity  of  the  steering  linkage,  the  connector 
pin  nut  must  be  securely  locked.  In  fact,  everything  pertaining 
to  the  steering  mechanism  must  be  absolutely  reliable. 

Tubular  and  Pressed  Steel  Axles— Tubular  front  axles  are 
generally  made  from  nickel  steel  tubing,  which  has  a  tensile 
strength  of  120,000  pounds  per  square  inch  and  may  be  worked  at 
12,000-15,000  pounds  per  square  inch.  Such  axles  have  the  same 
strength  in  the  horizontal  as  in  the  vertical  plane,  and  therefore 
are  not  easily  bent  by  striking  obstructions.  In  the  case  of  cars 
with  comparatively  wide  frames  the  spring  seats  may  be  forged 
integral  with  the  axle  ends,  which  are  pinned  and  brazed  or 


FIG.  271.— TIE  ROD  CONNECTOR. 


merely  clamped  to  the  axle  tube.  Some  designers  prefer  clamp- 
ing to  brazing,  because  in  the  latter  process  the  metal  is  likely 
to  be  overheated  and  thus  weakened.  In  smaller  cars  with  a 
comparatively  narrow  frame  this  scheme  is  not  praticable  and 
the  spring  seats  must  be  separately  clamped  or  pinned  and 
brazed  to  the  tube.  In  pressed  steel  axles  both  the  forged  axle 
ends  and  the  spring  seats  are  riveted  to  the  pressed  steel  part. 
For  the  axle  end  rivets  are  placed  both  vertically  and  horizontally. 
These  pressed  steel  axles  are  made  from  carbon  steel  stock,  as  a 
rule,  and  with  that  material  the  stress  should  be  limited  to 
10,000  pounds  per  square  inch. 

Manufacture  of  Front  Axles — The  chief  machining  opera- 
tions on  a  front  axle  are  the  facing  of  the  ends  of  the  steering 
heads  and  the  drilling  and  reaming  of  the  holes  for  the  pivot 
pins.  The  four  faces  of  an  Elliott  type  steering  head  are  usually 


FRONT  AXLES. 


409 


I 

C 


410  FRONT  AXLES. 

faced  in  one  operation  in  a  milling  machine  by  means  of  four 
milling  cutters  mounted  on  the  same  spindle  the  proper  distances 
apart.  If  the  production  is  carried  on  at  a  sufficiently  large 
scale,  a  special  double  milling  machine  finishing  both  ends  of  the 
axle  at  the  same  time  would  possess  considerable  advantage. 
Fig.  272  shows  the  method  employed  at  the  plant  of  the  Timken- 
Detroit  Axle  Co.,  Detroit,  for  boring  and  reaming  the  holes  for 
the  pivot  pin.  A  special  double  ended  machine  tool  is  used  for 
this  purpose,  which  permits  of  finishing  both  ends  of  the  axle 
at  the  same  time.  Each  spindle  of  the  tool  is  driven  separately 
by  belt  from  countershafts. 


CHAPTER  XV. 


THE  STEERING  GEAR. 

Historical— Instead  of  the  fifth  wheel  steering  arrangement 
used  on  horse  vehicles,  the  divided  axle  is  universally  employed 
on  automobiles.  This  was  invented  by  Lankensperger,  of  Munich, 
in  1817.  The  English  patent  on  it  was  taken  out  in  the  name  of 
Rudolph  Ackerman,  and  in  English  speaking  countries  the  gear,  in 
consequence,  has  come  to  be  known  as  the  Ackerman  steering  gear. 
A  refinement  of  this  steering  mechanism  for  automobile  purposes 
was  introduced  in  1878  by  Charles  Jeantaud,  a  French  carriage 
builder,  who  devised  what  is  known  as  the  Jeantaud  diagram. 
Jeantaud,  it  seems,  recognized  the  principle  that  if  the  vehicle  is  to 
turn  a  corner  without  sideward  slip  of  any  of  the  wheels,  the  link- 
age of  the  steering  wheels  must  be  so  arranged  that  the  axles  of  all 
the  wheels  produced  always  intersect  a  common  vertical  line,  the 
vertical  line  forming  the  momentary  axis  of  rotation.  Jeantaud 
found  that  in  order  to  approximately  fulfil  this  condition,  the 
steering  arms,  instead  of  being  parallel,  must  be  inclined  toward 
each  other  when  they  extend  to  the  rear  of  the  axle,  and  away 
from  each  other  when  they  extend  forward  of  the  axle;  and  his 
diagram,  which  is  intended  to  give  the  correct  inclination  of  the 
arms,  indicates  that  the  centre  lines  of  the  arms  produced  should 
meet  at  the  middle  of  the  rear  axle.  More  recent  investigations 
of  the  steering  problem  have  shown  that  with  the  ordinary 
trapeze  form  of  steering  linkage  it  is  impossible  to  absolutely 
satisfy  the  condition  of  correct  steering,  and  that  for  a  minimum 
error  for  the  whole  steering  range  the  point  of  intersection  of 
the  two  steering  arms  produced  lies  some  distance  in  front  of 
the  rear  axle. 

Theory  of  Steering  Mechanism — In  the  following  investiga- 
tion we  will  denote  the  length  of  the  wheel  base  by  W ';  the  dis- 
tance between  steering  pivots  by  L;  the  inclination  of  the  inner 
wheel  axis  by  a;  the  inclination  of  the  outer  wheel  axis  by  0;  the 
inclination  of  the  knuckle  arms  by  0 ;  the  length  of  the  arms  by  I. 

411 


412 


THE  STEERING  GEAR. 


Referring  to  Fig.  273,  it  will  be  seen  that 
a  c 

—  cot  a 

cd 

and 

be 

—  cot  ft 

cd 

Hence 

bc  —  ac/       L 

=  cot  /3  —  cot 


c 


FIG.  273. 


This  equation  enables  us  to  plot  the  required  values  of  /3  corre- 

L 
spending  to  different  values  of  ct  for  any  ratio  .     It  expresses 

the  condition  which  should  be  satisfied  by  the  gear,  but  furnishes 
no  guide  as  to  how  this  may  be  accomplished. 

Graphical  Solution  of  Steering  Problem — There  is  no  di- 
rect analytical  method  for  determining  the  most  advantageous 
angle  of  the  knuckle  arms,  and  some  graphical  method  is  usually 
employed.  By  laying  the  steering  diagram  off  on  the  drawing 
board  to,  say,  half  size,  a  sufficient  degree  of  accuracy  is  attained. 
Unfortunately,  for  small  deflections  of  the  front  wheels,  the  dis- 
tance of  the  point  of  intersection  of  the  wheel  axes  is  so  far  from 
the  axis  of  the  car  that  it  falls  far  outside  the  limits  of  an  ordi- 


THE  STEERING  GEAR. 


413 


nary  drawing  board,  and  accu- 
racy of  the  linkage  with  small 
deflections  is  of  special  import- 
ance, for  the  reason  that  the 
wheels  are  turned  through  a 
small  angle  very  much  oftener 
than  through  a  big  angle,  and  the 
car  generally  runs  at  a  much 
higher  speed  when  describing 
curves  of  large  than  of  small 
radius.  This  difficulty  may  be 
overcome  as  follows  (Fig.  274)  : 
From  points  a  and  b,  denoting 
the  steering  pivots,  draw  lines 
perpendicular  to  the  axles  which 
will  intersect  the  rear  axle  at 
e  and  /.  Next,  draw  a  line  from 
the  middle  point  g  of  the  front 
axle  to  point  e.  Then  lines  drawn 
from  the  pivot  points  a  and  b  to 
any  point  on  line  g  e  will  make 
with  the  front  axle  correspond- 
ing steering  angles.  This  may  be 
proven  as  follows: 


FIG.  274. 


and 


Of 

cot  a.  =  = 

ih 

bi 

cot  /3  =  — -  = 
ih 


ag  —  ig 


ag  +  ig 


But 

and  substituting, 


ik 

2ig 

.  r  .  cot  p  —  cot  a  = 

ih 
ig        ag 


ih 


cot  P  —  cot  a  = 


a  e 
2ag 


ac       ^    W 

Now  assume  steering  arms  of  a  definite  length  and  making 
a  certain  angle  with  the  longitudinal  vehicle  axis.  Next  deter- 
mine graphically  the  deflection  of  the  outer  wheel  for  various 
assumed  deflections  of  the  inner  wheel,  say,  8,  16,  24,  32,  40  and 
48  degrees,  for  these  steering  arms.  This  has  been  done  in 
Fig.  275  for  two  particular  cases.  The  -following  dimensions  were 
assumed  in  making  this  drawing:  L  =  50  inches;  I  =.7  inches 


414 


THE  STEERING  GEAR. 


THE   STERING  GEAR.  415 

and  angle  O  =  15  and  20  degrees,  respectively.  The  values  of 
angle  |8  were  determined  graphically  for  values  of  angle  a  of  8, 
16,  24,  32,  40  and  48  degrees,  respectively.  After  these  values  of 
angle  /3  had  been  found,  corresponding  angles  a  and  ft  were  laid 
off  on  opposite  ends  of  the  line  L.  Through  the  points  of  inter- 
section of  the  lines  describing  corresponding  angles  were  drawn 
curves,  one  for  the  15  degree  knuckle  arms  and  the  other  for  the 
20  degree  knuckle  arms.  These  may  be  called  steering  error 
curves,  because  their  deviation  from  the  diagonal  line  ge  (Fig. 
274)  indicates  the  error  in  the  steering  angles.  In  Fig.  275  the 

L 
diagonal  g  e  corresponding  to  the  value =  0.45  is  drawn  in.    It 

W 

will  be  seen  that  for  small  deflections  the  angle  of  the  outer 
wheel  is  too  large  with  both  15  and  20  degree  knuckle  arms. 
The  20  degree  knuckle  arm  gives  the  correct  deflection  of  the 
outer  wheel  at  about  26  degrees  of  the  inner  wheel,  and  the  15 
degree  knuckle  arm  gives  the  correct  deflection  of  the  outer 
wheel  at  46  degrees  deflection  of  the  inner  wheel.  Beyond  these 
points  the  angle  of  the  outer  wheel  is  too  small.  It  may  readily 
be  seen  from  this  that  the  most  advantageous  angle  of  the 
knuckle  arms  depends  upon  the  turning  range  of  the  inner  wheel. 
Thus,  if  the  motion  of  the  inner  wheel  were  limited  to  32 
degrees,  the  20  degree  knuckle  arm  would  be  the  best,  whereas 
if  the  range  of  motion  of  the  inner  wheel  were  as  large  as  45 
degrees,  the  angle  of  the  knuckle  arm  should  be  about  18  de- 

L 

grees— for  a  value  of  —  =  0.45. 

.  w 
In  order  to  use  this  method  for  the  practical  determination  of 

the  proper  knuckle  arm  angle,  steering  error  curves  for  differ- 
ent knuckle  arm  angles  and  lengths  should  be  laid  out  very 
carefully  for  permanent  use,  and  in  any  particular  case  the 

diagonal  g  e  corresponding  to  the  particular  value  of  ~^-~    should 

be  placed  on  the  chart  in  pencil,  when  the  most  advantageous 
knuckle  arm  angle  will  at  once  be  apparent. 

An  Analytical  Method — An  ingenious  analytical  method  of 
determining  the  deflection  of  the  outer  wheel  corresponding  to  a 
given  deflection  of  the  inner  wheel  has  been  published  by  Her- 
bert C.  Snow  (THE  HORSELESS  AGE  of  April  13,  1910).  A  short 
resume  of  this  method  follows : 

Four  different  cases  have  to  be  considered,  viz.,  with  the 
knuckle  arms  in  front  and  in  the  rear,  respectively,  and  with  the 
knuckle  arm  angle  6  greater  and  less  than  the  deflection  ft  of 


416 


THE  STEERING  GEAR. 


the  outer  wheel,  respectively.     In  Fig.  276  the  knuckle  arms  ex- 
tend to  the  rear  of  the  axle  and  angle  9  is  greater  than  /3.    In 
this  diagram  the  knuckle  arms  are  purposely  shown  abnormally 
long,  for  the  sake  of  greater  clearness.    Referring  to  the  Fig., 
M  =  L  —  2lsinO 


ga  —  l  cos  (a  + 
hi  =  jb  =  lsin 
jf  =  lcos(B  — 


Substituting  values  of  g  e  and  h  i, 

I  sin   (a  +  0)+Af  —  N  +  lsin 
Substituting  the  value  of  M, 

I  sin  (a  +  e)  +  L 
Transposing  and  dividing  by  /, 


—  /3)=L 


(65) 


FIG.  276. 

By  a  similar  process  of  reasoning  it  is  found  that  with  P  greater 
than  9  and  the  arms  extending  to  the  rear 
.    ,Q 0. .    /     i   m •    0 -A7"  /66\ 

with  P  smaller  than  6  and  the  arms  in  front  of  the  axle — 


sin  (0  —  p)  =  2  sin  9  —  sin  (6  -f  a)  — 


N 


(67) 


and  with  /3  greater  than  0  and  the  arms  in  front  of  the  axle 
sin  (ft  —  0)=  sin  (6  +  a)  —  2  sin  e  -f 


A 


.(68) 


These  various  equations  cannot  as  yet  be  solved  because  N  is 
not  known.  The  value  of  N  in  terms  of  known  factors  may  be 
found  as  follows:  O=-jf — jh. 

When   p   is   smaller  than   e, 

jf=lcos(e-?} 


THE  STEERING  GEAR.  417 

hence 

O  =  /  cos  (0  —  j8)  —  /  cos  (a  +  6)  = 

/  [cos  (0_/3)  —cos  (a  +  6)] (69) 

Similarly,  when  £  is  greater  than  0, 

//  =  /  cos  (]S  —  0)  and 

O  =  /  [cos  (|8  —  0)  —  07.S-  (a  +  0)] (70) 

In  every  case 

M  -  N  =  \/M2-  O2 
and 

AT  =  M  —  -\fj?  —  o2 (71) 

The  equations  thus  derived  permit  of  accurately  determin- 
ing the  angle  of  the  outer  wheel  corresponding  to  any  angle 
of  the  inner  wheel,  the  proportions  of  the  linkage  being  given. 
The  following  example  shows  its  method  of  application:  Sup- 
pose the  distance  L  between  pivots  to  be  50  inches ;  the  length 
/  of  the  knuckle  arms,  6.5  inches;  0,  20  degrees,  and  «,  30  de- 
grees, the  knuckle  arms  extending  to  the  rear  of  the  axle.  Then 
according  to  equation  (66)  ^ 

sin  (/3  —  20°)  =  sin  (20  +  30) °  —  2  sin  20° 

/ 

N 
Disregarding  the  term  —  for  the  moment  we  get  for  a  first 

/ 
trial  value 

sin  (£  —  20°)  =0.082. 

/3  =  24°  42'. 

Inserting  this  value  of  j8  in  equation  (70)  we  get 
O  =  6.5  (0.9966  —  0.6428)  =  2.2997, 
M  =  50  —  (2  X  6.5  X  0.342)  =  45.56 
and  inserting  these  values  in  equation  (71)  we  get 

N  =  0.053. 
Now  using  this  value  N  in  equation  (66)  we  get 

/3  =  25°  10'. 

The  calculations  could  be  continued  further,  but  Mr.  Snow 
has  shown  that  the  second  trial  value  is  correct  within  one  min- 
ute in  the  most  extreme  case,  which  is  as  high  a  degree  of  ac- 
curacy as  is  required  in  practical  work. 

Using   this   method,    Mr.    Snow    calculated   the    error    in    the 

steering  angle   for  each  of  the  turning  angles  25°   and  30°   of 

the  inner  wheel,  with  the  knuckle  arms  set  at  from  15°  to  30°, 

extending   both   to   the   front   and   the   rear,    using   four  ratios 

/ 

—  in  each  case,  viz.,  0.10,  0.12,  0.14  and  0.16.  The  results 
L 


418 


THE  STEERING  GEAR. 


of  these  calculations  are  plotted  in  Charts  IV  and  V.  These 
charts  give  the  best  value  for  the  angle  of  the  knuckle  arms 
for  limiting  turning  angles  of  33°  and  40°  of  the  outer  wheel, 

when  the  values  of  — -  and  —  are  known. 

rr  JLt 

General  Arrangement  of  Gears — Automobiles  are  steered 
by  means  of  hand  wheels,  whi'ch  in  the  case  of  pleasure  car^ 
are  located  at  the  top  of  a  rearwardly  inclined  steering  col- 
umn, and  in  the  case  of  trucks,  at  the  top  of  a  vertical  or 
nearly  vertical  column.  The  spider  of  the  hand  wheel  is  se- 

-asf- 


26° 


r 

>* 


t'£2& 


<%// 


V~.3O        .34  .36  .42  .4G  .SO  .S4          .£6         -G2 

CHART  IV. — PROPER  KNUCKLE  ARM  ANGLES  FOR  A  LIMITING  DE- 
FLECTION /3  OF  THIRTY-THREE  DEGREES. 

cured  to  a  shaft  which  generally  passes  down  inside  an  outer 
stationary  tube.  At  the  bottom  of  the  shaft  is  located  the  so- 
called  steering  mechanism  which  reduces  the  motion  of  the 
hand  wheel.  This,  in  the  great  majority  of  cases,  consists  of 
either  a  worm  and  worm  wheel  sector  or  a  worm  and  complete 
worm  wheel.  A  worm  and  nut  mechanism  is  also  used  to  quite 
an  extent,  particularly  abroad,  while  spur  pinion  and  rack,  and 
bevel  pinion  and  bevel  gear  sector  mechanisms  are  used  in  a  few 
cases. 


THE  STEERING  GEAR. 


419 


In  pleasure  cars  the  steering  motion  is  geared  down  in  such  a 
ratio  that  it  requires  from  one  to  one  and  a  quarter  complete 
turns  of  the  steering  hand  wheel  to  turn  the  front  wheels 
from  hard  over  one  way  to  hard  over  the  other  way  and  in 
trucks,  so  it  requires  from  one  and  one-half  to  two  complete 
turns.  The  linkage  connecting  the  steering  mechanism  with  one 
of  the  knuckles  is  generally  so  proportioned  that  the  steering  arm 
which  is  secured  to  the  steering  device  turns  through  an 
angle  of  about  60  degrees  while  the  road  wheels  are 'turned 


£6 


" 


V 

i 


m 


1&" 


CHART  V. — PROPER  KNUCKLE  ARM  ANGLES  FOR  A  LIMITING  DE- 
FLECTION /3  OF  FORTY  DEGREES. 

through  their  entire  range.  This  implies  a  reduction  ratio 
of  the  steering  mechanism  of  from  6 :1  to  12 :1,  according  to  the 
weight  and  speed  of  the  vehicle. 

Reversible  and  Non=Reversible  Gears — For  powerful, 
high  speed  cars  it  is  generally  considered  best  to  have  the 
steering  gear  back-locking  or  irreversible;  that  is  to  say,  so 
designed  that  any  shocks  received  by  the  road  wheels  will 
not  be  transmitted  to  the  steering  hand  wheel.  This  un- 
doubtedly makes  for  comfortable  driving  under  all  circum- 
stances, and  for  safety  in  driving  at  high  speed.  On  the  other 


420  THE  STEERING  GEAR. 

hand,  for  moderately  powered  cars  a  slightly  reversible  steer- 
ing gear  has  an  advantage,  because  it  greatly  reduces  the 
shocks  on  the  steering  mechanism,  as  well  as  on  the  front 
axle.  It  is  obvious  that  with  an  absolutely  irreversible  mech- 
anism any  shocks  received  by  the  front  wheels  are  entirely 
taken  up  by  the  steering  mechanism,  whereas  with  a  slightly 
reversible  mechanism  the  shocks  are  partly  transmitted  to  the 
steering  wheel,  and  the  strain  on  the  steering  members  is 
relieved  by  the  cushioning  effect  due  to  yielding  of  the 
driver's  arm.  There  is  no  fixed  angle  of  lead  of  the  worm 
below  which  the  worm  gear  is  non-reversible,  as  the  point 
where  it  becomes  reversible  depends  upon  the  materials,  the 
finish  and  the  state  of  lubrication  of  the  mechanism.  Assum- 
ing a  coefficient  of  friction  of  o.i  the  worm  gear  efficiency 
formula  given  in  a  previous  chapter  shows  that  a  worm  gear 
becomes  back-locking  when  the  angle  of  lead  drops  below 
6  degrees,  but  this  formula  takes  no  account  of  the  bearing 
friction.  Generally,  when  it  is  desired  to  make  the  steering 
mechanism  irreversible  the  angle  of  lead  is  made  from  8  to 
10  degrees,  whereas  for  a  slightly  reversible  gear  a  lead  angle 
of  12  to  16  degrees  is  chosen. 

Calculation  of  Worm  and  Wheel — Steering  mechanisms  of 
the  worm  and  sector  or  worm  and  wheel  types  are  calcu- 
lated by  means  of  the  formulae  for  worm  gearing  given  in  an 
earlier  chapter.  Since  the  steering  arm  usually  swings  only 
through  an  angle  of  60  degrees,  only  about  90  degrees  of  the 
worm  wheel  comes  in  contact  with  the  worm  teeth,  while 
the  front  wheels  are  moved  through  their  entire  turning 
range.  Formerly  it  was  customary  to  use  a  sector  embracing 
only  about  90  degrees  of  the  complete  wheel,  and  this  practice 
still  prevails  abroad,  but  in  recent  years  it  has  become  the 
custom  in  this  country  to  employ  a  complete  wheel,  the  shaft 
of  the  wheel  being  squared  where  the  steering  arm  is  se- 
cured to  it,  so  that  after  one  section  of  the  wheel  shows  ap- 
preciable wear,  the  wheel  can  be  turned  through  an  angle  of 
90  degrees  and  another  quarter  section  brought  into  action. 
The  wearing  portion-  of  the  worm  wheel  can  thus  be  renewed 
three  times  in  succession. 

Both  the  worm  and  the  wheel  of  a  steering  mechanism  are 
made  of  steel.  The  conditions  differ  from  those  under  which 
a  worm  gear  transmission  operates  in  that  mechanical 
strength  of  the  teeth  is  the  chief  consideration  rather  than 


THE  STEERING  GEAR.  421 

minimum  friction,  for  which  reason  steel  is  used  for  the  wheel 
instead  of  bronze.  The  worm  is  usually  case  hardened. 

As  regards  its  ability  to  sustain  tangential  loads,  the  worm 
wheel  of  a  steering  mechanism  does  not  differ  much  from  a 
spur  gear,  and  the  necessary  size  of  the  wheel  may  be  deter- 
mined by  a  method  similar  to  that  used  for  the  calculation  of 
spur  gears.  In  the  chapter  on  the  change  speed  gear  we  found 
that  the  maximum  safe  tangential  load  of  a  spur  gear  is  given 
by  the  equation 

w  =  Spfy, 

where  S  is  the  maximum  permissible  unit  stress;  p  the  circu- 
lar pitch;  /  the  face  width  and  y  a  constant.  The  constant  y 
may  be  neglected  in  this  case  because  the  number  of  teeth  used 
in  the  wheels  of  worm  steering  mechanisms  does  not  vary  much. 
Roughly  speaking,  the  face  width  /  is  proportional  to  the  pitch 
diameter  of  the  worm,  which  in  turn  is  proportional  to  the  dis- 
tance between  the  axes  of  worm  and  wheel.  Also,  the  tangential 
force  on  the  worm  wheel  acts  through  an  arm  equal  to  the  radius 
of  the  wheel,  which  is  also  proportional  to  the  distance  D  between 
the  axes  of  worm  and  wheel.  Hence,  the  moment  which  the 
worm  wheel  will  sustain, 

Mr    ~    DZ   P. 

On  the  other  hand,  the  maximum  turning  moment  which  will  be 
impressed  upon  the  worm  wheel, 

a  c 

Mi   ~   W 

b 

Where  W  is  the  maximum  weight  on  one  front  wheel;  a,  the 
distance  between  the  centre  plane  of  the  wheel  and  the  steering 
pivot;  b,  the  length  of  the  knuckle  arm  and  c,  the  length  of  the 
steering  arm.  Hence  we  may  write 

a  c 

W D2  p 

b 
Data  on  hand  shows  that  in  modern  pleasure  car  practice 


\W  a  c 

D  = J X  

\  ^nn         h  * 


(72) 

600         b  p 
and  in  motor  trucks  fitted  with  solid  tires 


/  W  a  c 

D  = J X  

\  i  ?no       h  f> 


(73) 

1,200        b  p 
Six  pitch  teeth  are  usually  employed  in  pleasure  car  steering 

gears,  and  four  pitch  teeth  in  gears  for  heavy  trucks.    The  worm 
is  made  with  from  two  to  four  threads.    Equations  (72)  and  (73) 


422  THE  STEERING  GEAR. 

are  useful  as  an  indication  of  the  capacity  of  different  gears. 
They  are  intended  to  be  used  only  in  connection  with  mechan- 
isms comprising  a  full  wheel;  when  a  sector  is  used  the  centre 
distance  for  a  certain  capacity  should  be  made  somewhat  greater, 
as  with  no  means  for  compensating  for  wear  of  the  teeth  it  is 
advisable  to  reduce  the  wear  by  keeping  down  the  unit  tooth 
pressure. 

We  will  now  illustrate  the  design  of  a  worm  and  wheel  steer- 
ing mechanism  by  the  example  of  a  gear  for  a  medium  sized 
touring  car  with  a  maximum  weight  of  750  pounds  on  one  front 
wheel  and  a  distance  of  2^4  inches  between  the  centre  plane  of 
the  wheel  and  the  pivot  axis.  We  may  assume  that  the  steering 
arm  and  knuckle  arm  are  of  equal  length.  If  the  pitch  of  the 
teeth  is  to  be  6,  then  the  required  centre  distance  of  worm  and 
wheel  is 

'J75°       2^5  =2.57  rn^s- 
600  ^  o .  52 

Now  suppose  that  the  worm  has  three  threads  and  an  angle  of 
lead  of  14  degrees,  so  as  to  be  slightly  reversible.  Then  the 
worm  pitch  diameter  will  be 

3X0.5236      =2.o67  inches, 
3.1416X0.242  _^ 

A  wheel  with  21  teeth  would  give  a  reduction  of  7  to  1  and 
would  require  a  little  over  one  complete  turn  of  the  steering 
wheel  to  turn  the  steering  arm  60  degrees.  Such  a  wheel  would 
have  a  pitch  diameter  of 

21  x  0-5236  =  3>6o5  inches 

3. 1416  X  0.9703 
The  centre  distance  then  would  be 

2.067  +  3.605  =  2>836  inch€Sf 

2 

This  is  a  little  more  than  the  centre  distance  required  according  to 
equation  (72).  If  the  centre  distance  had  come  ®ut  a  little  too 
small  we  could  have  chosen  one  or  two  more  teeth  for  the  wheel 
and  made  the  calculation  over. 

The  included  angle  of  the  wheel  face  is  usually  made  between 
45  and  60  degrees. 

It  is  somewhat  difficult  to  arrive  at  a  basis  for  dimensioning 
the  steering  gear,  since  the  forces  which  the  different  parts 
are  called  upon  to  transmit  are  indeterminate.  These  forces, 
of  course,  increase  directly  with  the  weight  on  each  front 
wheel,  and  substantially  as  the  distance  between  the  centre 
plane  of  the  wheel  and  the  steering  pivot  axis.  The  forces 


THE  STEERING  GEAR.  423 

also  increase  with  the  maximum  speed  of  the  car,  but  rather 
than  to  introduce  the  speed  into  formulae  for  the  dimensions 
of  the  gear  it  will  be  advisable  to  use  different  constants  in 
such  formulae  for  gears  intended  for  different  classes  of  vehi- 
cles. The  author  has  found  that  in  average  pleasure  car 
practice  the  torsional  strength  of  the  worm  wheel  shaft  at  the 
elastic  limit  of  the  material  is  about  seven  times  greater  than 
the  product  of  the  weight  on  each  front  wheel  into  the  dis- 
tance between  the  centre  plane  of  the  wheel  and  the  steering 
pivot  axis,  and  in  truck  practice  three  and  one-half  times 
greater.  These  coefficients  will  serve  as  a  basis  for  portion- 
ing the  worm  wheel  shaft,  the  steering  arm  and  the  drag 
link.  The  proper  size  of  the  worm  wheel  shaft  can  be  deter- 
mined first,  and  the  other  parts  enumerated  can  be  made  of 
such  size  that  they  are  strained  to  their  elastic  limit  when  the 
shaft  is  strained  to  this  point. 

The  usual  formula  for  the  torsional  strength   of  a  round 
shaft  is 

T  =  0.196  d5  S. 

If  the  shaft  is  square  at  one  end  for  fitting  the  steering  arm 
its  strength  is  reduced  to  about 

T  =  o.i4  da  S. 

If  now  we  make  6"  equal  to  the  elastic  limit  of  the  material 
then  for  pleasure  cars, 

7  ^0  =  0.14  d3  S 
and 


=y 


50  Wa  .     . 

Y~  (72) 

while  for  motor  trucks 

(73) 

These  formulae  are  to  be  used  only  for  the  conventional  con- 
struction, as  they  would  fail  if  the  steering  pivot  were  in  the 
centre  of  the  wheel. 

The  worm  wheel  shaft  is  preferably  forged  integral  with  the 
wheel,  owing  to  the  fact  that  space  in  the  direction  of  the 
axis  of  the  worm  wheel  is  limited,  at  least  if  the  shaft  is 
mounted  in  plain  bearings,  as  is  usually  the  case,  and  it  is 
therefore  difficult  to  secure  the  worm  wheel  or  sector  rigidly 
by  keying  or  otherwise. 


424  THE  STEERING  GEAR. 

Bearings. — Each  of  the  two  parts  of  a  worm  and  wheel  steer- 
ing gear  is  subjected  to  both  thrust  and  radial  loads,  the  thrust 
load  on  the  worm  being  particularly  great.  Ball  thrust  bearings 
are  nearly  always  provided  on  the  worm  shaft,  whereas  the 
radial  load  on  this  shaft  is  generally  taken  on  plain  bearings, 
though  in  some  instances  cup  and  cone  bearings  are  used  to  take 
both  the  radial  and  thrust  load.  This  applies  to  both  the  worm 
and  the  wheel.  The  cup  and  cone  bearing  would  seem  to  haye 
special  advantages  in  this  case,  and  it  is  somewhat  surprising 
that  it  is  not  more  extensively  used.  In  the  majority  of  cases  the 
wheel  shaft  is  mounted  in  plain  bearings  and  has  plain  thrust 
washers  of  bronze  or  hardened  steel.  In  gears  for  the  cheaper 
grade  of  cars  the  shaft  of  the  worm  wheel  or  sector  is  generally 
supported  in  one  bearing  only,  but  this  is  not  as  satisfactory  as 
bearings  on  opposite  sides  of  the  wheel.  The  total  bearing  length 
of  the  worm  wheel  shaft  is  made  from  three  diameters  in  the 
case  of  a  single  bearing  to  as  high  as  six  diameters  in  the  case  of 
two  bearings.  From  four  and  one-half  to  five  diameters  is  good 
average  practice.  It  is  very  essential  that  proper  provisions  be 
made  for  the  lubrication  of  the  shaft  bearings,  as  excessive  wear 
due  to  want  of  lubrication  is  common  and  very  annoying. 

In  order  to  provide  means  for  adjusting  the  mesh  of  the  worm 
and  the  wheel,  eccentric  bearing  bushings  are  sometimes  placed 
on  the  wheel  shaft,  which  can  be  turned  in  the  hubs  of  the  hous- 
ing and  secured  in  any  position.  Such  an  adjustment  permits  of 
compensating  for  errors  in  machining  the  housing,  but  not  for 
wear  of  the  worm  and  wheel. 

Steering  Shaft. — The  steering  shaft  to  which  the  worm  is 
secured  presents  quite  an  engineering  problem.  The  size  of 
the  worm  limits  the  external  diameter  of  this  hollow  shaft,  and 
its  internal  diameter  is  limited  by  the  fact  that  it  must  contain 
three  concentric  members,  viz.,  a  stationary  tube  which  supports 
the  sector  on  which  the  spark  and  throttle  levers  move,  the 
throttle  control  tube  and  the  spark  control  shaft,  together  with 
bearing  bushings  for  the  latter  two.  Yet,  the  steering  shaft  must 
have  an  appreciable  wall  thickness  because  the  worm  and  the 
steering  hand  wheel  have  to  be  keyed  or  otherwise  rigidly  se- 
cured to  it. 

The  worm  calculated  in  the  foregoing  example,  which  had 
a  pitch  diameter  of  about  2^  inches  and  a  bottom  diameter  of 
about  Hi,  is  about  as  small  a  worm  as  it  used  in  steering 


THE  STEERING  GEAR. 


425 


gears.  The  largest  diameter  of  steering  shaft  that  this  will 
take  is  about  il/%  inches  outside  diameter.  If  the  control 
shafts  are  to  be  placed  concentric  with  the  steering  shaft  the 
largest  possible  wall  diameter  of  the  latter  is  one-eighth  inch. 
The  different  concentric 'members  could  then  be  made  of  the 
following  dimensions:  Spark  shaft,  five-sixteenth  inch  diam- 
eter; throttle  control  shaft,  one-half  inch  o.  d.  and  three- 
eighth  inch  i.  d.;  stationary  tube,  three-quarters  inch  o.  d., 
five-eighths  inch  i.  d. 


JT31 


FIG.  277. — WORM  AND  WHEEL  STEERING  MECHANISM  WITH  ONE 
PART  CASING. 


In  steering  gears  of  large  size,  where  the  worm  diameter 
does  not  limit  the  outside  diameter  of  the  hollow  shaft  so 
closely,  a  tube  with  a  three-sixteenth  inch  or  even  thicker  wall 
is  used,  which  permits  of  securely  keying  the  worm  and  hand 
wheel  to  it,  and  the  middle  portion  of  the  tube  is  turned 
down  in  the  lathe  for  weight  economy. 

For  fastening  the  worm  to  its  shaft  the  best  plan  would 
seem  to  be  to  broach  it  out  and  mill,  say,  four  grooves  into 
the  outside  of  the  steering  shaft,  but  the  most  common  plan 
seems  to  be  to  use  a  single  key. 


426 


THE  STEERING  GEAR. 


Steering  Gear  Cases — There  are  three  general  types  of 
steering  gear  cases.  These  cases  may  be  cast  in  a  single 
piece,  with  a  separate  end  plate,  as  shown  in  Fig.  277;  they 
may  be  split  in  the  plane  through  the  worm  axis  and  per- 
pendicular to  the  wheel  axis,  as  in  Fig.  278,  gr  in  the  plane 
of  the  wheel  axis  and  perpendicular  to  the  worm  axis,  as  in 
Fig.  279.  The  tendency  in  American  practice,  especially  in 
the  low  priced  class,  seems  to  favor  the  first  construction. 
The  worm  can  be  introduced  either  from  the  top  or  bottom, 
and  the  wheel,  of  course,  is  introduced  from  the  side.  One 
of  the  thrust  bearings  rests  against  the  wall  of  the  case  and 


FIG.  278. — WORM  AND  WHEEL  STEERING  MECHANISM  WITH  VER- 
TICALLY DIVIDED  CASING. 

the  other  against  a  threaded  bushing  screwing  into  the 
casing.  This  bushing  is  made  slightly  larger  in  diameter  than 
the  worm,  and  is  locked  in  position  by  a  clamp  screw  which 
contracts  the  neck  of  the  case.  The  casing,  as  well  as  the 
removable  end  plate,  is  cast  with  a  bearing  hub.  which  is 
properly  strengthened  by  ribs.  The  thrust  on  the  worm  wheel 
shaft  is  taken  up  on  thrust  washers. 

These  cases  are  generally  made  of  malleable  iron,  with  a 
wall  thickness  of  three-sixteenth  inch.     The  gears  and  bear- 


THE  STEERING  GEAR. 


427 


ings  are  lubricated  by  means  of  grease  contained  in  the  case, 
and  a  plugged  hole  is  provided  in  the  case  for  replenishing 
the  grease  supply  therein  at  intervals.  However,  the  bearings 
should  preferably  be  provided  with  separate  grease  cups,  par- 
ticularly the  top  one. 

Housings  split  in  one  of  the  centre  planes  are  somewhat 
neater  in  appearance,  but  involve  more  machine  work.  The 
halves  must  be  doweled,  and,  of  course,  several  more  bolts 
are  required  for  the  joint  than  where  only  an  end  plate  has 
to  be  secured.  This  construction  also  facilitates  assembling, 


FIG.  279. — WORM  AND  SECTOR  STEERING  MECHANISM  WITH  CASING 
DIVIDED  THROUGH  THE  SECTOR  Axis. 

as  the  steering  post  can  be  completely  assembled  before  the 
housing  is  put  in  place,  and,  besides,  the  latter  can  be  made 
somewhat  more  compact,  as  it  is  not  necessary  to  introduce  the 
worm  and  thrust  bearings  from  the  end. 

Fig.  279,  which  shows  the  housing  divided  in  a  plane  per- 
pendicular to  the  worm  shaft,  also  illustrates  the  use  of  a 
sector  instead  of  a  complete  wheel.  Where  a  sector  is  used  it 
is  customary  to  provide  set  screw  stops,  limiting  the  motion 
of  the  sector,  which  makes  steering  stops  on  the  front  axle 
unnecessary. 


428 


THE  STEERING  GEAR. 


Screw  and  Nut  Type  Steering  Gears — The  screw  and  nut 
steering  gear  consists  of  a  multiple  square  threaded  screw 
and  a  corresponding  nut,  with  trunnions  on  its  outside, 
carrying  square  trunnion  blocks  located  in  slots  in  the  arms 
of  a  forked  lever,  which  is  keyed  or  otherwise  secured  to  the 
steering  arm  shaft,  or  made  integral  therewith.  The  size 
of  the  screw  depends  somewhat  on  whether  the  control  shafts 
are  to  be  concentric  with  the  steering  post  or  outside  of  it. 


FIG.  280. — SCREW  AND  NUT  TYPE  STEERING  GEAR. 

Let  us  call  the  distance  between  the  screw  and  steering  arm 
shaft  axes  a.  Then  if  the  steering  arm  is  to  swing  through  a 
maximum  range  of  60  degrees,  or  30  degrees  to  either  side 
of  its  central  position,  the  motion  b  of  the  nut  along  the 
screw  from  the  central  to  one  of  its  limiting  positions  must  be 
such  that 

—  =  tan  30°  =  0.577 
a 

Thus,  if  0  =  3  inches,  then 

b  =  3  x  0.577  =1,731  inches 


THE  STEERING  GEAR.  429 

and  the  total  motion  of  the  nut  along  the  screw  is  twice  this. 
or  3.462  inches.  If  the  screw  be  given  a  lead  of  2^  inches 
then  the  steering  hand  wheel  will  have  to  be  turned  through 


2.5 

in  order  to  turn  the  front  wheels  through  their  entire  range. 
Now,  suppose  the  screw  has  an  outer  diameter  of  2  inches. 
Then  the  angle  of  the  thread  at  the  circumference  will  be 
such  that 

tan  6  —  -  ^  -  =  o.  398 
2X  3-1416 

6  =  21°  42'. 

With  a  lead  of  2.5  inches  and  quadruple  thread  the  thickness 
of  the  tooth  will  be 


X  0.929  —  0.29  inch. 


8 
The  depth  of  the  thread  is  usually  made  equal  to  the  width. 

Double  Screw  Adjustable  Gears  —  It  has  been  attempted  to 
overcome  the  difficulty  encountered  in  cutting  the  thread  in 
the  nut  by  casting  a  babbitt  thread  in  a  steel  sleeve  provided 
with  holes  to  insure  a  good  hold  for  the  babbitt.  Some  of  the 
gears  based  on  this  principle  have  proven  failures,  probably 
because  the  thread  contract  surfaces  were  too  scanty.  Of  course, 
even  a  slight  amount  of  wear  in  the  steering  mechanism  is  ob- 
jectionable, because  it  entails  a  very  considerable  play  in  the  hand 
wheel.  Various  schemes  have  been  tried  for  taking  up  wear  in 
steering  mechanisms,  but  most  of  them  are  either  too  expensive 
for  commercial  work  or  else  are  objectionable  for  other  reasons. 
A  very  neat  mechanical  solution  of  the  adjustment  problem 
is  embodied  in  the  double  screw  type  of  the  Gemmer  Mfg. 
Co.,  illustrated  in  Fig.  281.  Secured  to  the  steering  shaft  D 
is  a  steel  shell  C,  which  is  provided  with  a  left  hand  square 
screw  thread  on  its  outer  surface  and  a  right  hand  thread  on 
its  inner  surface,  the  pitch  of  both  threads  being  the  same. 
When  shaft  D  is  turned  right  handedly,  sliding  member  B  is 
moved  down  and  sliding  member  E  up.  These  two  sliding 
parts  press  against  opposite  ends  of  a  double  armed  lever  F 
secured  to  the  steering  arm  shaft  and  cause  the  latter  to  turn 
in  its  bearings,  the  power  being  transmitted  through  sliding 
member  B  when  shaft  D  is  turned  right  handedly,  and 


430 


THE  STEERING  GEAR. 


through  sliding  member  E  when  shaft  D  is  turned  left  hand- 
edly.  Any  wear  on  the  threads  can  be  taken  up  by  screwing 
the  bushing  A  further  into  the  housing. 

Another  combination  often  used  in  steering  gears  is  a  screw 
and  nut,  together  with  a  rack  and  spur  wheel  sector,  the  rack 
teeth  being  cut  on  the  outside  of  the  nut. 


1 


FIG.  281. — DOUBLE  SCREW  TYPE  STEERING  GEAR. 

Bevel  Gear  Steering  Mechanism — Other  mechanisms  for 
reducing  the  steering  motion  include  a  bevel  pinion  and  sector, 
a  spur  pinion  and  sector,  a  spur  pinion  and  rack  and  a  planetary 
set.  All  of  these  gears  are  completely  reversible,  and  with  a 
car  fitted  with  any  of  them  it  is  impossible  for  the  driver  to 
take  his  hands  off  the  wheel  while  in  motion,  and  he  feels  the 
road  shocks  more  than  with  the  type  of  gear  previously  de- 
scribed. These  steering  mechanisms,  therefore,  are  suited  only 
to  cars  of  moderate  speed  capabilities  or  those  having  such  an 
arrangement  of  the  steering  pivots  that  practically  no  motion 
can  be  transmitted  from  the  wheel  to  the  steering  mechanism. 


THE  STEERING  GEAR. 


431 


Owing  to  the  reversibility  of  these  gears  the  gear  reduction 
should  be  made  as  large  as  space  limitations  permit. 

Fig.  282  illustrates  the  Reo  steering  gear  which  is  of  this  type. 
The  thrust  of  the  bevel  gear  sector  is  taken  up  on  a  steel  roller, 
and  the  steering  motion  is  limited  in  a  very  simple  manner  by 
leaving  a  portion  at  each  end  of  the  sector  without  teeth.  Bevel 
gear  type  of  steering  mechanisms  have  less  need  for  housings 
than  the  worm  and  wheel  type,  but  some  designers  enclose  them 
also. 

Support  of  Steering  Gear. — If  the  knuckle  arm  to  which 
the  drag  link  connects  is  below  the  front  axle  the  steering 


FIG.  282.— REO  BEVEL  STEERING  GEAR. 


arm  can  be  placed  inside  the  frame  member — a  construction 
found  on  a  considerable  number  of  European  cars.  Where 
the  knuckle  arm  is  above  the  axle  this  arrangement  is  impos- 
sible, because  the  front  spring  would  interfere  with  the  drag 
rod. 

In  this  connection  it  is  to  be  remembered  that  with  the  drag 
link  outside  the  frame  it  limits  the  possible  steering  motion  to- 
ward the  side  on  which  the  steering  gear  is  located,  as  the  front 
wheel  will  rub  against  the  drag  link  before  touching  any  other 
part.  This  disadvantage  may  be  overcome  by  placing  the  drag 
link  crosswise  of  the  frame.  In  motor  trucks  having  the  motor 
located  underneath  the  driver's  seat  the  steering  mechanism 


432 


THE  STEERING  GEAR. 


naturally  comes  in  the  right  position  for  a  transverse  drag  link, 
and  in  touring  cars  it  can  be  brought  into  the  proper  position  by 
giving  the  steering  post  a  large  inclination.  In  any  case,  the 
aim  in  laying  out  the  steering  connection  should  be  to  minimize 
the  effect  of  front  spring  action  on  the  steering  gear.  With  a 
transverse  drag_link  the  link  should  be  substantially  horizontal 
when  the  car  carries  a  normal  load,  whereas  with  a  fore-and-aft 
drag  link,  with  the  car  under  normal  load,  the  axis  of  the  drag 
link  produced  should  pass  through  the  centre  of  the  front  spring 
eye — supposing  the  front  spring  to  be  pivoted  to  the  frame  in 
front  and  shackled  at  the  rear. 

In  touring  cars  the  steering  gear  housing  usually  comes  in 
a  rather  cramped  position  between  the  engine  and  the  frame. 
It  may  be  so  placed  that  the  worm  wheel  shaft  passes  either 
through  the  web  of  the  frame  channel,  above  the  channel 
or  below  the  channel.  In  most  cases  the  shaft  passes  right 
through  the  frame  member.  The  housing  is  generally  bolted 
to  the  frame  side  member,  being  provided  with  a  bracket 
which  fits  into  the  opening  of  the  channel.  Again,  the  hous- 
ing may  be  bolted  to  the  top  of  the  side  member,  to  an 
engine  arm  or  to  a  cross  member  of  the  frame.  A  rigid 

support  is  necessary ;  and,  besides, 
it  is  well  to  remember  that  holes 

g-F^H^I-R— \     rffr^Jtn  through   the   flanges   of   a   frame 

7/^xpjy     f^TTI      channel  greatly  reduce  its  strength, 

whereas  holes  through  the  centre 
of  the  web  have  practically  no 
weakening  effect. 

Steering  Arm — The  steering 
arm  in  a  touring  car  is  generally 
from  7  to  9  inches  long.  The 
knuckle  arm  in  most  designs  is 
made  as  long  as  the  location  of 
the  front  springs  permits,  and  the 
steering  arm  the  same  length  or 
slightly  longer.  In  a  worm  and 
complete  wheel  type  of  steering 
gear  the  steering  arm  is  always  fit- 
ted to  the  squared  end  of  the 
wheel  shaft,  so  as  to  permit  of 
turning  the  wheel  through  a  quar- 
ter circle.  The  hub  of  the  arm  is 
split  and  clamped  on  the  shaft,  the 


FIG.   283. — STEERING    ARM. 


THE  STEERING  GEAR.  433 

clamping  bolt  passing  slightly  beneath  the  surface  of  the  shaft. 
When  a  worm  wheel  sector  is  used  and  the  housing  is 
divided  in  the  plane  through  the  sector  shaft  the  steering 
arm  and  shaft  may  be  forged  integral,  with  a  flange  sector 
on  the  shaft  to  which  the  worm  wheel  sector  is  bolted.  Oc- 
casionally, the  steering  arm  is  bent  so  that,  although  its  hub 
is  located  inside  the  frame,  its  connection  to  the  drag  link 
comes  outside  the  frame,  so  as  to  avoid  interference  with  the 
spring.  A  typical  design  of  steering  arm,  with  the  usual  pro- 
portions, is  illustrated  in  Fig.  283.  It  will  be  found  that  if 
this  arm  is  made  of  the  same  material  as  the  wheel  shaft  it 
is  of  substantially  the  same  strength  as  the  squared  portion 
of  the  shaft.  When  a  worm  wheel  sector  is  employed  instead 
of  a  complete  wheel  the  steering  arm  usually  is  secured  to  its 
shaft  with  a  tapered  joint — a  Woodruff  key  and  castellated  nut 
being  used. 

Drag  Link  and  Connectors — The  drag  link,  which  in  tour- 
ing cars  usually  extends  directly  fore-and-aft  and  in  motor 
trucks  and  cars  of  the  raceabout  type  crosswise  of  the  frame, 
is  usually  made  of  the  same  cross  section  as  the  tie  rod.  This 
practice  is  logical,  at  least  if  the  tie  rod  is  located  back  of  the 
axle  and  the  drag  link  is  of  about  the  same  length.  However,  if 
the  highest  weight  economy  is  desired  the  proper  size  of  this  tube 
can  be  calculated  by  means  of  Rankine's  formula  for  columns, 
proportioning  it  so  that  its  material  will  be  strained  to  the  elastic 
limit  when  the  rod  is  subjected  to  a  thrust  equal  to  the  quotient 
of  the  torsional  strength  of  the  steering  arm  shaft  by  the  length 
of  the  steering  arm.  In  the  better  grades  of  cars,  particularly 
those  provided  with  non-reversible  steering  gears,  it  is  customary 
to  introduce  cushion  springs  in  the  drag  link  joint  so  as  to  relieve 
the  shock.  A  length  of  tube  of  enlarged  diameter  is 
screwed  over  the  end  of  the  tube  forming  the  main  part  of 
the  drag  link,  or  is  pinned  to  it.  As  shown  in  Fig.  284,  in- 
serted into  this  connector  housing  are  the  following  parts 
in  the  order  named :  A  coiled  spring,  a  spring  block  with  a 
spherical  depression,  the  ball  end  of  the  steering  arm,  an- 
other spring  block,  another  coiled  spring  and  a  screw  plug 
secured  by  a  cotter  pin.  In  this  design  the  ball  is  passed 
through  a  hole  far  enough  to  the  end  of  the  connector  hous- 
ing so  that  the  ball  can  never  get  opposite  it  after  all  the 
parts  are  in  place.  Sometimes  the  slot  in  the  housing  through 
which  the  steering  arm  passes  extends  entirely  to  the  end 
of  the  housing,  in  which  case  a  screw  cap  is  used  instead  of 


434 


THE  STEERING  GEAR. 


FIG.  284. — BALD  AND  SOCKET  SPRING  CUSHIONED  CONNECTOR. 

a  plug  to  close  the  end  of  the  housing.  The  spring  cushioned 
joint  is  generally  placed  at  the  steering  gear  end  of  the  drag  link, 
the  joint  at  the  opposite  end  being  made  similar,  but  without  the 
springs.  Both  joints  are  generally  enclosed  in  a  laced  leather 
boot  which  is  filled  with  grease. 

Fig.  285  illustrates  a  front  end  connector  of  English  design. 
It  is  of  the  ball  and  socket  type,  but  entirely  different  in  prin- 
ciple from  the  connector  shown  in  Fig.  284.  The  ball  is  held 
between  two  steel  blocks,  which  are  inserted  into  a  fitting  of  the 
general  form  of  a  chain  link.  The  blocks  are  held  between  one 
end  of  this  link  and  the  end  of  the  connector  rod,  which  latter 


FIG.  285. — DRAG  LINK  FORWARD  CONNECTOR. 


THE  STEERING  GEAR. 


435 


passes  through  a  hole  through  the  hub  at  the  opposite  end  of 
the  link.  The  chain  link  and  connector  rod  are  secured  together 
by  means  of  a  gland  nut  with  differential  threads,  the  thread  on 
the  hub  of  the  link  being  much  coarser  than  that  on  the  rod. 
Thus,  when  the  nut  is  screwed  over  the  threads  on  the  rod  and 
the  hub,  although  both  are  right-handed  threads,  the  link  will  be 
moved  relatively  to  the  rod,  and.  thus  the  socket  blocks  will  be 
forced  against  the  ball.  When  they  have  been  properly  adjusted 
the  nut  is  locked  by  means  of  a  split  pin. 

Universal  joints  are  necessary  at  both  ends  of  the  drag 
link,  because  the  steering  arm  moves  in  a  vertical  plane  and 
the  knuckle  arm  in  a  horizontal  plane,  but  instead  of  ball 


FIG.  286. — FORKED  CONNECTOR. 

and  socket  joints,  forked  joints  are  sometimes  used.  These 
are  somewhat  simpler  in  construction,  and  larger  bearing 
surfaces  can  be  obtained  than  with  ball  and  socket  joints, 
but  they  are  not  so  easily  enclosed  in  a  grease  filled,  laced 
leather  boot,  and  are  generally  lubricated  by  means  of  a 
special  grease  cup.  The  grease  cup  may  be  screwed  into  the 
cross  piece,  as  shown  in  Fig.  286,  or  into  the  end  of  the  horizontal 
pin. 

Steering  Wheel — Steering  hand  wheels  are  made  14  inches 
in  diameter  for  very  small  cars,  16  inches  for  medium  sized 
cars,  18  inches  for  large  touring  cars,  and  as  high  as  20  inches 
for  heavy  trucks.  The  rims  are  made  of  either  hardwood  or 
hard  rubber.  The  section  is  generally  oval,  ixi^  inch  and 
il/ixil/2  inches  being  common  sizes.  The  spider  is  made  of  brass 


436 


THE  STEERING  GEAR. 


or  aluminum,  with  either  three  or  four  spokes — generally  four. 
In  commercial  vehicle  practice  malleable  iron  spiders  are  used. 
The  spokes  of  brass  and  malleable  iron  spiders  are  mostly  made 
of  oval  section,  but  the  spokes  of  aluminum  spiders  are  made  of 
channel  section  or  of  T-section  with  large  fillets  to  facilitate 
buffing.  For  a  16  inch  wheel  with  brass  spider  the  spokes  are 
made  about  l^xfys  inch  near  the  hub  and  tapering  down  to 
y%K$s  inch  near  the  rim.  In  an  aluminum  spider  for  the  same 
diameter  wheel,  the  spokes,  if  of  channel  or  T-section,  are 
made  about  ?/£  inch  deep  near  the  hub  and  y^  inch  near  the  rim. 


FIG.  287. — STEERING  WHEEL  WITH  ALUMINUM  SPIDER 
AND  BENT  WOOD  RIM. 


There  are  two  general  designs  of  wood  rims.  The  most 
commonly  used  type,  illustrated  in  Fig.  287,  is  secured  to  the 
arms  of  the  spider  by  means  of  wood  screws.  The  other  form, 
used  more  particularly  abroad  and  in  the  higher  grade  cars  in 
this  country,  has  a  ring  cast  integral  with  the  spider,  which  is 
let  into  a  groove  turned  in  a  part  of  the  wooden  rim  (see  Fig. 
288).  The  rims  are  made  in  different  ways.  In  one  construc- 
tion, illustrated  in  Fig.  287,  the  whole  rim  is  made  of  a  single 
piece  of  wood.  First  a  solid  piece  of  wood  of  square  section 


THE  STEERING  GEAR. 


437 


and  the  requisite  length  is  sawed  out,  and  its  ends  are  cut  with 
wedge-shaped  teeth  about  y^  inch  wide  and  I  to  1^4  inches  deep. 
It  is  then  turned  down  to  a  circular  or  oval  section,  steamed 
and  bent  to  a  circle  of  the  right  size  to  bring  the  pointed  tenons 
together,  when  they  are  glued  and  firmly  pressed  together  in  a 
special  clamp  in  which  the  rim  is  left  until  dry.  Specially  flexible 
woods  are  used  for  this  construction,  as  most  woods  do  not  al- 
low of  bending  to  such  a  small  radius.  Instead  of  making  the 
entire  rim  in  one  piece,  it  may  be  made  in  halves,  with  joints  of 
the  type  above  described.  A  quarter  inch  dowel  pin  through  the 


FIG.  288. — STEERING  WHEEL  WITH  LAMINATED  WOOD  RIM  AND 
OVAL  ARM  SPIDER  WITH  INTEGRAL  RIM. 

centre  of  the  joint  makes  it  more  secure.     Fig.  287  shows  two 
methods  of  securing  the  rim  to  the  spokes  of  the  spider. 

Another  method  of  making  the  rims  consists  in  building  them 
up  of  segments.  For  the  more  expensive  cars,  rims  of  mahogany, 
walnut  or  ebony  are  extensively  used.  As  a  rule,  three  layers  of 
segments  of  four  or  six  to  the  circle  are  used,  six  being  pre- 
ferable, as  there  is  not  so  much  end  grain  where  the  segments 
are  joined  together.  After  the  segments  are  sawed  out  they 
are  glued  up  three  deep  into  rings,  and  are  then  turned  up  in  a 


438 


THE  STEERING  GEAR. 


lathe.  They  are  secured  in  the  lathe  either  by  being  glued  to  a 
wooden  face  plate  with  a  sheet  of  newspaper  between,  or  else 
by  means  of  a  number  of  screws.  Of  course,  if  the  spider  is 
cast  with  an  integral  ring,  the  final  turning  up  of  the  rim  has  to 
be  done  with  the  spider  in  place. 

Vulcanized  rubber  steering  wheel  rims  are  coming  into  ex- 
tensive use.  The  rubber  is  vulcanized  onto  a  ring  cast  in- 
tegral with  the  spider,  and  is  provided  on  the  inside  with  de- 
pressions to  fit  the  fingers,  and  on  the  outside  with  small 


FIG.  289.—  HARD  RUBBER  RIM  WHEEL. 


evenly  spaced  projections,  so  as  to  enable  the  driver  to  ob- 
tain a  firm  grip  of  the  wheel.  A  typical  hard  rubber  steering 
wheel  is  illustrated  in  Fig.  289. 

In  pleasure  cars  the  steering  shaft  is  generally  enclosed  in  a 
brass  tube  of  iV  inch  wall  thickness.  Referring  to  Fig.  290,  this 
tube  is  set  into  a  recess  formed  in  the  adjusting  nut  at  the  top 
of  the  steering  gear  and  usually  forms  a  tight  fit  in  a  bracket  se- 
cured to  the  dashboard  or  to  the  toolboard.  At  the  top  it  receives 
a  bushing  for  the  steering  shaft,  or  it  may  extend  into  a 


THE  STEERING  GEAR. 


439 


recess  turned  in  the  hub  of  the  steering  wheel,  in  which  case 
the  hub  holds  the  casing  concentric  with  the  shaft  and  no  bush- 
ing is  required.  In  some  designs  the  steering  shaft  case  ex- 
tends down  to  the  dash  bracket  only,  and  in  commercial  vehicles 
it  may  be  entirely  omitted. 

There  is  a  great  deal  of  variation   in  the  inclination  of  the 
steering   column,   depending   upon   the    relative    location   of   the 


FIG.  290. — STEERING  COLUMN. 

steering  mechanism  and  the  driver's  seat.  In  standard  touring 
car  practice  it  is  usually  inclined  about  45  degrees,  and  in  the 
more  rakish  types  of  cars,  such  as  raceabouts,  about  60  de- 
grees. In  order  that  the  driver  may  be  able  to  easily  enter  his 
seat  the  steering  wheel  rim  should  not  come  closer  than  8  inches 
to  the  front  edge  of  the  seat  cushion. 

Adjustable    Steering    Column— Owing    to    the    fact    that 
drivers  vary  a  great  deal   in  stature,  some  manufacturers  con- 


440  THE  STEERING  GEAR. 

sider  it  expedient  to  make  the  rake  of  the  steering  column  ad- 
justable. This  practice  is  particularly  prevalent  in  England, 
where  bodies  are  built  to  purchasers'  specifications,  and  it  is 
possible  that  this  is  another  reason  for  providing  adjusting 
means,  as  the  relation  of  the  seat  to  the  column  determines  the 
comfort  of  the  driver  to  a  large  degree.  To  make  the  steering 
column  adjustable,  the  bearing  hubs  of  the  steering  gear  case 
are  mounted  in  trunnion  supports  on  the  frame  and  the  column 
passes  through  a  slot  in  the  dashboard  or  toeboard,  clamping 
means  being  provided  to  secure  it  in  different  positions. 


CHAPTER  XVI. 


CONTROL. 

Spark  and  Throttle  Control — The  conventional  location  ot 
the  spark  and  throttle  control  levers  is  on  top  of  the  steering 
column.  A  sector  of  hardened  steel  is  secured  by  screws  to  a 
double  armed  brass  bracket  which  is  fixed  to  a  stationary  tube 
concentric  with  the  steering  post.  Usually  the  bracket  is  clamped 
to  the  tube,  though  some  makers  fasten  it  by  means  of  a  screw. 
The  spark  lever  is  usually  secured  to  the  central  rod  by  pinning, 
and  the  throttle  lever  to  the  tube  surrounding  this  rod  by  clamp- 
ing. 

The  angular  extent  of  the  sector  may  be  anything  from  about 
75  degrees  to  a  complete  circle.  The  former  size  of  sector  is 
used  if  the  connections  from  the  lower  ends  of  the  spark  and 
throttle  shafts  are  to  be  made  direct  by  levers  and  links.  This 
is  the  simplest  construction,  but  it  is  obvious  that  a  much  finer 
control  is  possible  if  the  range  of  the  finger  levers  is  greater, 
and  for  this  reason  a  reducing  gear  of  some  kind  is  usually  in- 
troduced in  the  control  mechanism  at  the  bottom  of  the  steering 
column.  In  American  touring  car  practice  it  is  customary  to 
use  a  sector  of  180  degrees  or  slightly  less,  whereas  in  European 
practice  90  degree  sectors  are  very  common.  The  180  degree 
sectors  are  so  placed  that  the  ends  of  the  sector  lie  in  the  fore 
and  aft  direction,  the  sector  extending  to  the  right  from  the 
steering  post.  Forward  motion  of  the  levers  advances  the  spark 
and  opens  the  throttle. 

Some  means  must  be  provided  for  automatically  holding  the 
control  levers  in  any  position  in  which  they  are  placed.  The 
most  common  arrangement  consists  in  providing  the  steel  sector 
with  ratchet  teeth  on  both  edges,  and  the  finger  levers  with  a 
spring  pressed  pawl  which  engages  with  the  teeth  on  the  sector. 
The  ratchet  teeth  are  cut  with  an  angle  of  about  90  degrees,  so 
that  if  a  tangential  force  is  applied  to  the  lever  arm  the  pawl  will 
slide  freely  over  the  notched  sector.  A  typical  design  of  control 
levers  is  shown  in  Fig.  291. 

441 


442 


CONTROL. 


In  another  design  of  control  levers  an  arm  of  spring  metal  is 
riveted  to  a  brass  hub  and  provided  with  a  hard  wood  or  hard 
rubber  knob  on  the  outer  end.  In  this  case  the  flat  side  of  the 
steel  is  placed  vertically,  and  the  under  and  upper  edges  are 
notched,  wedges  secured  to  the  levers  by  means  of  rivets  engag- 
ing with  these  notches.  Probably  a  somewhat  neater  design 
would  be  obtained  by  saw  slotting  the  lugs  on  the  lever  centres, 
placing  the  spring  steel  arms  in  the  saw  slot,  and  countersinking 


FIG.  291.— RATCHET  CONTROL. 


the  holes  for  the  rivet  heads.  In  the  design  shown  in  Fig.  292 
the  throttle  lever  must  be  pressed  down  and  the  ignition  lever 
raised  up  in  order  to  move  them  easily.  By  using  two  sectors  it 
is  possible  to  arrange  the  levers  so  that  both  of  them  can  be 
released  by  pressing  on  them,  which  method  of  operation  may  be 
considered  preferable,  for  the  reason  that  the  weight  of  the  hand 
naturally  rests  on  the  levers.  The  ratchet  teeth  should  not  be 
over  ^s  inch  deep,  so  the  lever  can  be  moved  with  as  little  noise 
as  possible. 


CONTROL. 


443 


Fig.  293  illustrates  a  design  of  friction  levers.  On  top  of  the 
stationary  tube  in  the  steering  column  is  mounted  a  cylindrical 
brass  box.  with  a  horizontal  slot  on  one  side  through  which  the 
control  levers  extend.  An  extension  of  each  lever  arm  to  the 
opposite  side  of  its  axis  carries  a  friction  segment  which  is 
pressed  against  the  inner  wall  of  the  cylindrical  housing  by  a 
coiled  spring.  The  pressure  of  this  spring  can  be  adjusted  by 
means  of  a  nut  and  lock  nut. 


FIG.  292. — SPRING  LEVER  CONTROL. 

Ball  Wedge  Locking  Device. — Fig.  294  illustrates  a  mechan- 
ism widely  used  on  European  cars  for  securely  holding  control 
levers  in  any  position  in  which  they  may  be  set.  The  mechanism 
consists  of  a  stationary  housing  A,  which  is  usually  part  of  the 
bracket  by  which  it  is  supported.  E  is  the  control  lever  and  B 
the  operated  lever.  Formed  integral  with  lever  E  are  two  lugs 
F  F,  extending  between  the  wall  of  the  housing  A  and  a  cam  C 
on  the  shaft  of  lever  B.  In  the  recess  between  the  two  lugs  F  F 
are  located  two  steel  balls  with  a  coiled  spring  between  them. 
The  cam  surface  and  the  inner  wall  surface  of  the  housing  are 
eccentric,  and  are  so  spaced  relative  to  each  other  that  the  steel 


444 


CONTROL. 


balls  do  not  quite  contact  with  the  lugs  FF  when  no  pressure 
is  being  exerted  on  the  lever  E.  The  wedging  effect  of  the  balls 
between  the  two  non-concentric  surfaces  securely  locks  the  lever 
B  in  place.  It  will,  moreover,  be  seen  that  lever  B  is  locked 
against  motion  in  either  direction,  each  ball  locking  it  against 
motion  in  one  direction.  If  lever  E  is  turned  in  a  particular 
direction,  one  of  the  lugs  FF  presses  against  the  ball  near  it. 
slightly  compressing  the  spring,  and  the  other  lug  then  abuts' 
against  the  arm  of  lever  B,  so  that  any  further  motion  of  lever 
E  entails  a  corresponding  motion  of  lever  B.  One  of  the  pre- 
cautions to  be  observed  in  the  design  of  the  device  is  to  see  that 


FIG.  293. — FRICTION  CONTROL. 

the  clearance  between  the  balls  and  the  lugs  FF,  when  lever  E 
is  not  under  pressure,  is  slightly  less  than  the  clearance  between 
these  lugs  and  the  arm  of  lever  B.  The  inner  wall  of  the  hous- 
ing and  the  cam  surface  are  grooved  to  fit  the  contour  of  the 
balls,  so  as  to  distribute  the  pressure  over  a  larger  surface  and 
prevent  injury  to  the  balls.  The  condition  necessary  that  the 
lever  may  be  locked  securely  is  that  when  the  ball  is  in  the  locking 
position  the  tangents  at  its  two  points  of  contact  make  with  each 
other  an  angle  which  is  less  than  twice  the  angle  of  friction. 

When  applied  to  a  control  gear  on  top  of  the  steering  column, 
lever  B  in  Fig.  294  is  replaced  by  a  small  lug  on  cam  C,  with 


CONTROL. 


445 


which  the  lugs  F  F  may  engage,  and  cam  C  is  fastened  to  the 
central  shaft  by  which  the  motion  is  transmitted.  This  locking 
device  is  used  even  for  such  important  parts  as  the  emergency 
brake  lever,  but  where  the  effort  to  be  transmitted  is  consider- 
able two  or  three  pairs  of  balls  are  used  and  a  cam  with  three 
cam  surfaces. 

Owing  to  the  fact  that  the  control  levers  have  a  motion  of 
about  150  degrees,  whereas  a  lever  arm  transmitting  motion 
through  a  link  does  not  work  advantageously  beyond  a  range 
of  about  90  degrees,  the  motion  of  the  control  shafts  has  to  be 
reduced  in  some  way,  and  this  is  now  generally  accomplished 
by  means  of  a  pair  of  small  bevel  gears  or  bevel  gear  sectors 
at  the  bottom  of  the  steering  column.  As  shown  in  Fig.  295, 


C 


FIG.  294. — BALL  WEDGE  CONTROL  LOCK. 

the  bevel  gears  or  sectors  are  secured  to  the  lower  ends  of 
concentric  vertical  shafts  carried  in  a  bearing  which  is  gener- 
ally clamped  to  a  bracket  cast  integral  with  the  steering  gear 
housing.  Sometimes  the  bearing  bracket  is  formed  integral 
with  the  bottom  plate  of  the  steering  gear  housing  to  which  the 
stationary  tube  carrying  the  finger  lever  sector  is  fixed.  Where 
there  are  several  concentric  shafts,  as  in  this  case,  if  they  are  to 
be  prevented  from  rattling,  it  is  necessary  that  a  bearing  bushing 
be  provided  for  each  shaft,  rather  than  to  rely  upon  the  fit  of 
one  shaft  in  the  other. 

Instead  of  a  bevel  pinion  and  sector,  a  pair  of  screws  and 
nuts  may  be  used  for  transmitting  the  control  motion  at  the 
bottom  of  the  steering  gear  housing.  The  more  elaborate  de- 


446 


CONTROL. 


signs  provide  a  screw,  nut  and  trunnion  mechanism  of  the  same 
type  as  used  for  steering  cars,  the  whole  mechanism  being 
inclosed.  In  the  simpler  designs  the  nut  and  its  trunnions  are 
dispensed  with,  a  pin  projecting  laterally  from  a  lever  arm  ex- 
tending into  a  spiral  slot  cut  yi  a  cylinder  secured  to  the  con- 
trol shaft. 

Bowden  Wire  Mechanism — The  Bowden  wire  mechanism, 
which  is  used  to  some  extent  for  the  control  of  the  throttle  and 
the  timer,  more  particularly  in  England,  consists  mainly  of  two 


295. — CONTROL  REDUCING  GEAR. 


parts,  a  closely  coiled  and  practically  incompressible  spiral  wire, 
constituting  what  is  termed  the  outer  member,  and  a  practically 
inextensible  wire  cable  threaded  through  the  above,  and  known 
as  the  inner  member.  The  principle  of  the  mechanism  is  illus- 
trated in  Fig.  296.  A  is  the  actuating  lever;  B,  the  operated 
lever;  C,  the  inner  member;  D,  the  outer  member;  E,  an  adjust- 
able stop ;  F,  a  lock  nut,  and  G,  the  abutments  or  brackets.  It  is 
obvious  that  since  the  outer  member  is  incompressible  and  the 
inner  member  inextensible,  if  the  lever  A  is  moved  around  its 


CONTROL. 


447 


fulcrum,  the  end  of  lever  B  will  be  moved  with  relation  to  the 
abutment  G. 

Control  Levers  on  Steering  Post. — Fig.  297  illustrates  a 
construction  in  which  the  control  levers  are  mounted  on  the 
steering  post  underneath  the  steering  wheel.  This  design  is  used 
more  particularly  on  commercial  cars  and  the  lower  priced  pleasure 
vehicles,  being  probably  the  simplest  possible  arrangement  of  the 
control.  The  shafts  for  the  spark  and  throttle  are  arranged  con- 
centrically and  are  supported  in  bearings  secured  to  the  steering 
column.  A  sector  is  also  cast  integral  with  the  top  supporting 


FIG.  296. — BOWDEN  WIRE  MECHANISM. 

bearing,  and  the  control  levers  are  pressed  into  contact  with  the 
sector  by  means  of  a  coiled  spring  surrounding  the  power  part 
of  the  central  control  shaft,  the  spring  pressing  the  tubular 
shaft  upward  and  the  solid  shaft  downward.  Lever  arms  are 
secured  to  the  lower  ends  of  these  shafts,  and  connection  to  the 
throttle  and  tinier  is  made  by  links  direct.  The  sector  on  which 
the  levers  move  extends  over  an  angle  of  about  90  degrees,  and 
is  usually  placed  in  front  of  the  steering  column,  as  this  location 
is  most  convenient  for  making  connections  from  the  lower  ends 
of  the  shafts. 


448 


CONTROL. 


FIG.  297. — CONTROL  LEVERS  ON  STEERING  POST. 


FIG.  298.— CONTROL  JOINTS. 


CONTROL.  449 

Control  Joints. — In  the  connecting  linkage,  if  two  lever  arms 
to  be  connected  swing  in  the  same  plane  a  forked  connector  is 
employed,  and  a  standard  for  such  connector  yokes  and  eyes  has 
been  worked  out  by  the  Society  of  Automobile  Engineers.  If 
the  two  arms  do  not  swing  in  the  same  plane,  as  is  often  the 
case,  a  ball  and  socket  type  of  joint  is  used.  The  links  of  the 
control  mechanism  are  generally  made  of  cold  rolled  steel,  seven- 
thirty-seconds  or  one-quarter  inch  in  diameter,  and  one  part  of 
the  joint  is  screwed  over  the  end  of  the  rod.  In  cars  sold  at 
a  very  low  price  the  end  of  the  rod  is  sometimes  bent  at  right 
angles  and  passed  through  a  hole  of  slightly  greater  diameter 
in  the  end  of  the  arm,  a  split  pin  being  passed  through  the  end 
of  the  rod.  This  type  of  joint  rattles  more  or  less,  and  is  not 
very  satisfactory.  Fig.  298  shows  three  types  of  ball  and  socket 
joints  for  carburetor  and  spark  connections.  The  one  shown  at 
A  consists  of  a  brass  socket  and  a  steel  ball,  the  brass  socket 
being  bored  out  and  having  the  edges  spun  in  after  the  ball  is 
in  place.  A  well  designed  type  of  joint  is  shown  at  B.  This 
resembles  a  steering  drag  link  joint,  except  that  only  one  spring 
is  used  whose  object  is  to  firmly  press  the  socket  blocks  against 
the  ball.  No  play  can  develop  in  a  joint  of  this  type,  and  there- 
fore it  remains  free  from  rattle.  The  joint  shown  at  C  is  similar 
except  that  the  spring  is  missing  and  D  shows  the  simple  joint 
above  referred  to. 

In  cars  which  have  two  independent  ignition  systems  it  is  neces- 
sary to  make  connection  from  the  spark  control  to  the  two 
timers,  and  this  is  often  accomplished  by  securing  a  bell  crank  to 
the  top  of  the  short  vertical  shaft  shown  in  Fig.  295.  On  the  other 
hand,  many  cars  have  been  built  in  recent  years,  particularly 
abroad,  without  manual  spark  advance,  and  in  that  case  only  a 
single  control  lever  has  to  be  accommodated  on  the  steering  post. 

Usually  at  least  one  of  the  devices  that  must  be  connected  to 
the  control  levers  is  located  on  the  opposite  side  of  the  chassis 
from  the  steering  column,  and  tfie  connection  to  it  must  then 
pass  either  around  or  through  the  engine.  A  short  shaft  may  be 
carried  in  bearing  brackets  secured  to  the  forward  side  of  the 
dashboard,  or  to  uprights  rising  from  the  sub- frame,  but  some 
manufacturers  pass  a  shaft  transversely  through  the  engine  base 
underneath  one  of  the  crankshaft  bearings,  thus  eliminating  un- 
necessary linkage.  Great  care  is  latterly  exercised  by  designers 
to  make  the  control  linkage  as  simple  and  unobstrusive  as  pos- 
sible. Thus,  in  the  Fiat  car  the  connecting  link  to  the  timer  is  run 
inside  the  sub-frame  channel. 


450 


CONTROL. 


Accelerator  Pedals— Most  modern  cars  are  fitted  with  both 
hand  and  foot  control  of  the  throttle.  The  throttle  foot  control 
device,  generally  referred  to  as  the  accelerator,  assumes  different 
forms,  and  three  designs  are  illustrated  in  Figs.  299  and  300. 


FIG.  299. — ACCELERATOR  PEDALS. 

The  one  shown  at  A,  Fig.  299,  is  a  pedal  of  the  piano  type, 
being  pivoted  to  a  bracket  secured  to  the  dashboard.  At  B,  Fig. 
299,  is  shown  an  accelerator  which  has  a  motion  around  a  vertical 
axis,  and  is  operated  by  a  sideward  motion  of  the  forward  part 


CONTROL. 


451 


of  the  foot,  with  the  heel  resting  on 
the  footboard.  The  bearing  bracket 
for  this  lever  is  also  secured  to 
the  dashboard,  but  in  a  much  lower 
position  than  that  for  design  A.  In 
the  design  shown  in  Fig.  300  a 
foot  button  is  used,  together  with 
a  bell  crank  carried  by  a  bracket 
secured  to  the  under  side  of  the 
toe  board.  All  three  designs  have 
their  adherents  and  all  give  satis- 
factory results. 

Throttle  Linkage. — The  method 
of  connecting  up  the  throttle  with 
the  hand  and  foot  controls  is  illus-        FIG.  300. — ACCELERATOR 
trated  in  diagram  in  Fig.  301.     In  FOOT  BUTTON. 

this  figure  A  represents  the  lever  at  the  bottom  of  the  steer- 
ing column.  Through  the  boss  at  the  outer  end  of  this  lever 
passes  a  rod  which  joins  to  the  throttle  arm.  It  will  be  noticed 
that  arm  A  contacts  with  a  collar  on  the  control  rod  on  one 
side  and  with  a  coiled  spring  on  the  rod  on  the  opposite  side. 
The  accelerator  pedal  B  connects  with  the  throttle  lever  through 
a  control  rod  with  an  oblong  hole  at  one  end  through  which 
passes  a  pin  extending  laterally  from  the  arm  of  the  pedal.  The 
accelerator  pedal  is  normally  held  in  the  off  position  by  a  coiled 
spring  anchored  to  a  stationary  part  of  the  car. 

The  hand  control  mechanism  is  so  arranged  that  by  moving 
the  throttle  lever  on  top  of  the  steering  column  through  its  entire 
range  the  throttle  valve  is  only  about  half  opened,  and  the 


Fir,.  301. — DIAGRAM  OF  THROTTLE  CONTROL  LINKAGE. 


452 


CONTROL. 


throttle  can  only  be  fully  opened  by  depressing  the  accelerator 
pedal  B.  Operating  the  hand  lever  does  not  affect  the  position 
o.f  pedal  B,  because  the  control  rod  connecting  the  pedal  to  the 
throttle  arm  has  a  sliding  connection  with  the  pedal.  If  the 
throttle  is  fully  opened  by  means  of  the  accelerator  pedal  and 
the  driver  then  removes  his  foot  from  the  latter,  the  throttle 
will  return  to  the  position  for  which  the  hand  lever  is  set.  The 
spring  around  the  control  rod  which  connects  arm  A  to  the, 
throttle  arm  permits  of  fully  opening  the  throttle  by  means  of 
the  accelerator  pedal,  even  though  the  hand  throttle  lever  may 
be  set  in  the  position  corresponding  to  closed  throttle. 


FIG.  302.— GOVERNOR  THROTTLE  CONTROL  (AUTOCAR). 

Motor  trucks  generally  have  their  motors  fitted  with  gov- 
ernors and  require  a  special  control  mechanism.  Two  separate 
throttle  valves  may  be  used,  arranged  in  the  intake  passage  one 
above  the  other,  one  connected  with  the  governor,  the  other  con- 
nected to  hand  and  foot  controls,  or  simply  to  a  hand  control. 
The  throttle  controlled  by  the  governor  will  remain  fully  open 
until  the  motor  attains  the  speed  for  which  the  governor  is  set, 


CONTROL.  453 

when  it  will  begin  to  close.  A  simpler  and  more  common  method 
is  to  use  only  a  single  throttle  valve  to  which  the  governor  is 
connected  by  a  slotted  link.  Fig.  302  shows  the  mechanism  em- 
ployed on  the  Autocar  light  truck.  The  engme  is  ordinarily 
under  the  control  of  the  governor,  but  the  driver  may  close  the 
throttle  independent  of  the  governor. 

Clutch  and  Brake  Pedals — What  may  be  called  the  conven- 
tional arrangement  of  the  control  for  cars  fitted  with  sliding  gear 
transmissions,  comprises  two  pedals  located  on  opposite  sides  of 


FIG.  303. — TYPES  OF  CONTROL  PEDALS. 

the  steering  post,  the  one  on  the  left  being  the  clutch  pedal  and 
the  one  on  the  right  the  brake  pedal.  The  accelerator,  if  one  is 
provided,  is  placed  either  between  or  to  the  right  of  these  pedals 
for  operation  with  the  right  foot. 

Where  a  unit  power  plant  is  used  the  pedals  are  sometimes 
carried  on  the  clutch  housing,  but  the  more  common  plan  is  to 
provide  a  tubular  shaft  extending  partly  or  entirely  across  the 
frame,  which  is  carried  in  bearing  brackets  secured  to  the  frame. 
One  pedal  is  secured  to  this  shaft,  and  the  other  is  free  upon  it 
or  is  secured  to  a  hollow  shaft  telescoping  over  the  other  one. 

There  are  two  general  types  of  control  pedals,  the  straight 
and  the  bent  type,  as  illustrated  in  Fig.  303.  The  pedals,  of 


454 


CONTROL. 


course,  have  to  pass  through  the  toe  board,  and  if  they  are 
straight  they  require  a  long  slot  in  this  board,  whereas  if  they 
are  bent,  like  the  one  shown  at  A,  they  require  only  a  compara- 
tively small  hole  to  pass  through.  The  straight  pedal  is  lighter, 
but  the  bent  pedal  is  now  usually  used  because  there  is  an  ad- 
vantage in  having  the  driver's  compartment  closed  off  from  the 
engine  compartment  as  far  as  possible,  so  that  a  minimum  of  heat 
and  noxious  gases  from  the  engine  will  reach  the  occupants. 

Pedals  vary  in  effective  length  from  12  to  16  inches.  They  are 
generally  drop  forged,  and  the  section  is  made  either  I  or  T 
shaped,  oval  or  rectangular,  the  I  and  oval  sections  predominating. 


FIG.  304. — ADJUSTABLE  PEDALS. 

A  14  inch  pedal  usually  has  a  section  modulus  near  the  hub  of 
0.10  to  0.12,  while  near  the  pad  the  section  modulus  may  be  re- 
duced to  one-fourth  this  value.  Usually  the  dimension  of  the 
section  in  the  plane  of  greatest  stress  is  made  equal  to  about 
twice  its  other  dimension,  but  if  the  pedal  is  much  off-set  side- 
ways, as  is  sometimes  the  case,  it  must  be  made  stronger  later- 
ally. The  inclination  of  the  toe  board  in  American  touring  cars 
varies  from  35  to  45  degrees  and  this  approximately  deter- 
mines the  location  of  the  big  end  of  the  bent  pedal  in  the  position 
of  rest.  The  lighter  end  of  the  pedal  should  approximate  an  arc 
of  a  circle  with  the  pivot  axis  as  a  centre,  but  usually  it  is  turned 
so  the  pad  comes  somewhat  higher. 


CONTROL. 


455 


when  it  will  begin  to  close.  A  simpler  and  more  common  method 
is  to  use  only  a  single  throttle  valve  to  which  the  governor  is 
connected  by  a  slotted  link.  Fig.  302  shows  the  mechanism  em- 
ployed on  the  Autocar  light  truck.  The  engine  is  ordinarily  under 
the  control  of  the  governor,  but  the  driver  may  close  the  throttle 
independent  of  the  governor. 

Adjustable  Pedals — Considerable  attention  has  been  paid 
in  late  years  to  the  problem  of  comfort  for  the  driver,  and  this 
has  led  to  the  introduction  of  adjustable  pedals.  It  is  evident 


FIG.  305.— PEDALS  ADJUSTABLE  AT  THEIR  HUBS. 

that  a  pedal  suitably  located  for  a  tall  person  is  quite  incon- 
venient for  a  person  of  short  stature,  and  vice  versa.  These 
adjustable  pedals  are  usually  bent  at  a  right  angle.  Fig.  304  shows 
four  different  designs.  In  design  A  the  pad  is  secured  to  a 
round  rod  fitting  in  a  hole  through  the  upwardly  turned  part  of 
the  pedal  proper.  The  rod  is  drilled  with  a  number  of  transverse 
holes,  and  may  be  secured  in  any  one  of  several  positions  by 
means  of  a  through  bolt.  In  design  B  the  shank  of  the  pad 
is  threaded  and  is  clamped  in  the  hub  of  the  pedal  by  means  of 
two  nuts.  In  design  C  the  pedal  itself  is  made  of  I  section,  and 
the  pad  is  made  with  double  shanks  fitting  into  the  hollows  in  the 


456 


CONTROL. 


s'des  of  the  I,  the  two  parts  being  clamped  together  by  two 
through  bolts,  which  may  be  passed  through  different  holes  in 
the  pedal.  This  is  one  of  the  neatest  designs  of  adjustable  pedals, 
since  the  small  end  of  the  pedal  may  have  the  usual  curvature  and 
the  section  where  the  parts  are  joined  is  rectangular.  In  design 
D  the  shank  of  the  pad  is  threaded  and  screwed  into  the  drilled 
and  threaded  portion  of  the  pedal,  which  latter  is  slotted  and 
clamped  tight  on  the  shank. 

Control  pedals  may  also  be  adjusted  at  their  base,  and  two 
methods  of  accomplishing  this  are  illustrated  in  Fig.  305.  In 
either  case  there  are  a  free  and  a  tight  hub.  In  design  A  the 


FIG.  306.— PEDAL  PADS. 

tight  hub  has  two  lugs  with  coaxial  set  screws,  between  the 
points  of  which  is  located  a  lug  projecting  laterally  from  the 
pedal.  In  design  B  the  tight  hub  is  provided  with  a  slotted  sec- 
tor, cut  with  radial  grooves  on  one  side,  to  which  the  pedal  can 
be  clamped  in  different  positions. 

Pedal  Pads— Pads  are  either  secured  rigidly  to  the  pedal  or 
hinged  thereto.  In  the  former  case  they  are  usually  made  con- 
vex toward  the  rear,  so  that  as  the  pedal  turns  around  its  ful- 
crum a  section  of  the  pad  always  fits  squarely  against  the  sole 
of  the  driver's  shoe.  On  the  other  hand,  if  the  pad  is  hinged  to 
the  pedal  it  is  made  either  plane  or  slightly  concave,  and  in  the 
higher  grades  of  cars  a  spring  is  provided  to  hold  the  pad  in 


CONTROL.  457 

position  when  the  foot  is  removed,  so  as  to  prevent  rattling. 
Generally,  however,  the  swiveled  pad  is  allowed  to  hang  in  posi- 
tion under  its  own  weight.  Various  means  are  resorted  to  in 
order  to  prevent  slipping  of  the  foot  on  the  pad,  the  most  com- 
mon being  the  formation  of  diamond  shaped  points  by  forming 
V-shaped  grooves  on  the  surface  of  the  pad  diagonlly  in  two 
directions,  these  grooves  being  either  formed  in  a  drop  press  or 
cast  on.  (See  A,  Fig.  306.)  Another  method  consists  in  provid- 
ing the  pad  with  either  one  or  two  ears,  and  several  models  in 
the  higher  priced  class  are  provided  with  rubber  covered  pads. 
(B,  Fig.  306.)  These  rubber  coverings  are  used  together  with 
ears  on  the  sides  of  the  pad,  and  are  evidently  intended  to  pre- 
vent slipping  of  the  foot  in  the  direction  of  motion  only. 

There  is  absolutely  no  uniformity  with  regard  to  the  form  and 
dimensions  of  the  pads.  They  are  made  square,  rectangular,  oval 
and  round.  If  ears  are  provided  on  both  sides  the  pad  should  be 
at  least  3^  inches  wide,  but  if  no  ears  are  used  it  is  sometimes 
only  2l/2  inches  wide.  Some  pads  are  larger  in  the  fore  and  aft, 
others  in  the  transverse  direction. 

Most  clutches  are  disengaged  by  drawing  them  to  the  rear, 
and  in  the  case  of  such  clutches  the  pedal  shaft  is  located  on  top 
of  the  clutch  shaft.  However,  some  forms  of  clutches,  like  the 
inverted  cone  clutch,  are  disengaged  by  a  forward  motion,  and 
in  this  case  it  is  more  convenient  to  have  the  pedal  shaft  run 
underneath  the  clutch  shaft.  The  latter  arrangement  has  a 
further  advantage  in  that  if  the  service  brakes  act  on  the  rear 
wheels  the  brake  arm  on  the  pedal  shaft  has  to  extend  upward 
and  comes  in  a  more  convenient  position  if  the  shaft  is  located 
lower.  It  is  generally  endeavored  to  place  the  clutch  collar  and 
pedal  shaft  in  such  relative  positions  that  the  shipper  arms  on 
the  pedal  shaft  may  connect  directly  to  the  clutch  collar,  but  if 
this  is  not  possible  a  pair  of  links  may  be  interposed  between 
the  shipper  arms  and  the  clutch  collar.  The  leverage  of  the 
clutch  pedal  is  made  between  4  and  6,  depending  upon  the  clutch 
spring  pressure  and  structural  considerations. 

Interconnection  of  Clutch  and  Brakes— Formerly  it  was 
customary  to  interconnect  both  brakes  with  the  clutch,  so  that 
if  either  brake  were  applied  the  clutch  would  first  be  disengaged. 
The  idea  which  first  led  to  this  construction  was,  undoubtedly, 
that  if  the  driver  wants  to  stop  quickly  he  should  simultaneously 
disconnect  the  engine  and  apply  the  brake,  so  the  driving  effort 
of  the  engine  ceases  and  no  braking  effort  need  be  expended  in 
dissipating  the  energy  stored  in  the  flywheel.  The  intercon- 


458 


CONTROL. 


nection  is  usually  accomplished,  in  the  case  of  the  foot  brake, 
as  illustrated  in  Fig.  307,  a  projection  on  the  hub  of  the  brake 
pedal  engaging  with  a  projection  on  the  clutch  pedal  whenever 
the  brake  pedal  is  moved  to  apply  the  brake.  In  the  case  of  the 
hand  brake  the  connection  is  made  by  means  of  a  link  connect- 
ing arms  on  the  clutch  pedal  shaft  and  the  brake  lever  shaft,  re- 
spectively, with  a  sliding  joint  at  one  end  so  that  the  clutch 
can  be  disengaged  without  applying  the  brake.  One  disadvantage 
of  interconnection  is  that  with  this  scheme  it  is  not  possible  to 
use  the  engine  as  a  brake  and  use  the  mechanical  brakes  at  the 
same  time.  For  this  reason  the  interconnection  was  first  limited 


FIG.  307. — SERVICE  BRAKE  INTERCONNECTED  WITH  CLUTCH. 


to  one  brake  and  is  now  generally  dispensed  with  altogether. 
As  a  matter  of  fact,  with  the  clutch  and  brake  pedals  in  the 
usual  position,  it  becomes  second  nature  for  the  driver  to  press 
on  both  of  them  simultaneously  if  he  wants  to  make  a  quick 
stop. 

Single  Pedal  Control— In  several  makes  of  cars  the  clutch 
and  service  brakes  are  operated  by  a  single  pedal.  The  first  mo- 
tion of  the  pedal  releases  the  clutch  and  a  continued  motion 
applies  the  brake.  This  necessitates  a  special  operating  mechan- 
ism for  the  clutch.  One  arrangement,  involving  the  use  of  a 


CONTROL. 


459 


FIG.  308.— SINGLE  PEDAL  CONTROL,  TOGGLE  TYPE. 


FIG.  309.— SINGLE  PEDAL  CONTROL,  CAM  TYPE. 


460  CONTROL. 

toggle  mechanism,  is  illustrated  in  Fig.  308,  and  another  involving 
the  use  of  a  cam  mechanism  is  shown  in  Fig.  309.  In  the  former 
case  the  clutch  collar  is  moved  relatively  rapidly  during  the  first 
motion  of  the  pedal  and  more  slowly  as  the  motion  of  the  pedal 
proceeds.  With  a  cam  mechanism  the  motion  of  the  clutch 
collar  stops  entirely  after  the  clutch  is  fully  disengaged,  that 
portion  of  the  cam  coming  last  under  the  cam  follower  being  con- 
centric. In  order  to  prevent  an  unduly  large  release  motion  of  the 
clutch  bands  it  is  well  to  provide  a  sliding  joint  at  the  forward 
end  of  the  brake  rod  (Fig.  308).  This  combination  of  clutch  and 
brake  control  in  a  single  pedal  works  very  satisfactorily,  but,  of 
course,  the  pedal  must  have  a  somewhat  greater  range  of  motion 
than  when  it  operates  either  the  clutch  or  brake  alone.  The  two 
pedal  control  has  however  practically  become  standardized  and  it 
is  likely  that  single  pedal  control  will  disappear  entirely. 

Pedal  Shaft  Assembly. — In  some  designs  of  cars  employing 
a  housing  for  the  clutch,  the  clutch  pedal  is  supported  by  this 
housing  and  the  brake  pedal  by  a  bracket  secured  to  the  frame 
side  member.  In  cars  with  a  sub-frame  the  pedal  shaft  bearings 
can- be  secured  to  this  frame,  whose  top  surface  is  usually  1  to  1J4 
inches  above  the  clutch  axis.  Some  designers  secure  these  bear- 
ing brackets  to  the  front  side  of  a  frame  cross  member  and 
others  to  the  inside  of  the  frame  side  channels. 

Right,  Left  and  Centre  Control.— Formerly  the  steering 
column  was  nearly  always  placed  on  the  right  side  of  the  car,  and 
the  hand  levers  for  operating  the  change  gear  and  emergency 
brakes  were  located  just  outside  the  driver's  seat  on  the  right. 
Lately,  however,  more  and  more  cars  have  the  steering  post  on 
the  left  hand  side  and  the  hand  levers  in  the  centre.  Centre  con- 
trol may  also  be  combined  with  right  hand  drive,  and  left  hand 
control  with  left  hand  drive.  The  argument  in  favor  of  left  steer- 
ing is  that  with  the  rule  of  the  road  compelling  drivers  to  keep 
to  the  right,  they  can  much  better  gauge  the  clearance  when 
meeting  other  vehicles,  if  they  are  seated  on  the  left  side.  On 
the  other  hand,  the  driver  is  at  a  disadvantage  when  overtaking  a 
vehicle  or  drawing  up  at  the  curb,  as  he  is  then  on  the  "off" 
side.  The  advantage  of  control  levers  on  the  left  side  is  that  if  the 
vehicle  is  drawn  up  alongside  a  curb  both  the  driver  and  front  seat 
passenger  can  get  into  the  car  without  first  walking  half  way 
around  it.  However,  if  the  levers  are  on  the  left  hand  side  they 
must  be  operated  by  means  of  the  left  hand,  which  usually  is  not 
as  dexterous  as  the  right  hand.  This  is  one  of  the  reasons  for 


CONTROL. 


461 


the  increasing  popularity  of  centre  control.  Another  reason  is 
that  if  the  change  gear  lever  is  located  at  the  centre  it  may  be 
mounted  directly  on  top  of  the  change  gear  box,  thus  doing 
away  with  superfluous  connections.  Finally,  if  the  gear  and  brake 
levers  are  in  the  centre  the  outside  of  the  body  is  smoother  or 
"cleaner." 


FIG.  310. 
THUMB  LATCH  LEVER. 


FIG.  311. 
SPOON  LATCH  LEVER. 


Control  Levers. — Brake  and  change  gear  hand  levers  are 
generally  drop  forged  with  a  rectangular,  oval  or  I  section,  but 
cast  steel  or  bronze  levers  are  also  used.  In  pleasure  cars  the 
length  of  these  levers  generally  varies  between  20  and  24  inches, 
depending  upon  the  height  of  the  seat  The  maximum  pressure 
which  a  driver  is  ever  likely  to  exert  against  these  levers  is  100 


462  CONTROL. 

pounds.  Thus,  if  the  length  of  the  lever  from  the  axis  to  the 
middle  of  the  handle  be  20  inches,  the  bending  moment  at  a  dis- 
tance of  1  inch  from  the  axis  is  2,000  pounds-inches.  Now,  let 
us  suppose  that  the  section  is  to  be  rectangular,  with  a  height 
twice  the  width.  Then,  for  a  stress  in  the  material  of  15,000 
pounds  per  square  inch,  the  equation  of  moments  is 

b  d*  d3 

15,000 =  15,000  —  =  2,000 

6  12 

<f  =  1.6 

d  =  1.17— say,  1  3/16  inch 

b  =  19/32  inch 
An  elliptic  section  of  twice  the  height  as  the  width  has  a  sec- 

ds 
tion  modulus  of  —  approximately,  and  the  necessary  height  d 

20 

for  the  above  case  figures  out  to  1.385 — say,  \Y%  inches.  For 
light  cars  the  section  of  the  levers  can  be  calculated  on  the  basis 
of  a  maximum  pressure  of  50  pounds,  because  on  these  cars  less 
effort  is  required  to  operate  the  gears  and  brakes  and  the  driver 
knows  that  he  cannot  expend  his  whole  strength  on  the  levers. 

The  change  gear  lever  of  selective  type  change  gears  moves 
in  an  H  sector  or  gate,  and  does  not  require  a  latch  to  hold 
it  in  position.  However,  a  latched  lever  is  always  used  with 
the  progressive  gear  control,  and  the  emergency  brake  lever  is  also 
provided  with  a  latch.  There  are  two  general  types  of  latch 
levers,  illustrated  in  Figs.  310  and  311,  respectively.  The  former 
is  known  as  the  thumb  latch  and  the  latter  as  the  spoon  latch. 
The  operation  of  these  latches  is  self-evident  and  need  not  be 
described.  Both  levers  illustrated  are  designed  as  brake  levers, 
and  it  may  be  pointed  out  that  if  the  lever  is  a  "push  lever, ' 
applying  the  brakes  as  the  driver  pushes  it  away  from  himself, 
the  latch  spoon  must  be  on  the  forward  side  of  the  grip,  whereas 
if  it  is  a  "pull  lever"  the  latch  spoon  must  be  on  the  back.  The 
hand  grip  is  generally  made  of  circular  section,  and  often  it  is 
covered  with  a  brass  tube  which  is  screwed  or  welded  on.  Plating 
the  grips  has  proven  unsatisfactory,  as  even  a  heavy  coat  of  plate 
soon  wears  off.  If  no  brass  casing  is  used  the  handle  is  gener- 
ally made  tapering,  with  the  largest  diameter  at  the  top.  For  all 
except  the  smallest  cars  the  handle  can  be  made  $4  mch  in 
diameter  if  parallel,  and  from  ^  to  ^  inch  if  tapering. 

The  two  levers  are  generally  arranged  to  turn  about  a  com- 
mon pivot  axis,  and  the  brake  lever  is  the  one  farthest  away 
from  the  driver.  Near  its  big  end  it  is  provided  with  a  central 


CONTROL. 


463 


FIG.  312. — SLIDING  LEVER  SELECTIVE  GEAR  COVT 


464  CONTROL. 

slot  through  which  passes  the  ratchet  sector.  Ball  ended  change 
gear  levers  are  now  used  to  quite  an  extent.  In  England  balls 
of  hardwood  are  sometimes  forced  over  the  top  ends  of  the 
levers  and  held  in  place  by  screws.  The  levers  are  often  bent 
laterally  because  of  the  bulging  form  of  the  body  and  in  order 
that  there  may  be  plenty  of  clearance  between  the  grips  of  the 
two.  It  is  also  a  good  plan  to  make  the  brake  lever  of  such 
length  that  its  grip  comes  somewhat  higher  than  that  of  the 
gear  lever. 

Selective  Control. — There  are  three  general  systems  of  se- 
lective control.  The  first  of  these  comprises  a  sliding  shaft 
to  which  the  control  lever  is  rigidly  secured  and  which  at  its 
inner  end  carries  a  downwardly  extending  arm  which  is  adapted 
to  engage  into  a  slot  on  one  or  the  other  of  the  sliding  bars. 
A  typical  control  of  this  type  is  illustrated  in  Fig.  312.  The  gear 
control  lever  A  is  clamped  to  the  hollow  shaft  B  which  at  its 
opposite  end  carries  the  arm  C,  whose  free  end  is  adapted  to 
engage  into  slots  on  the  slider  bars  DE.  Lever  A  moves  in  the 
sector.  When  it  is  in  the  slot  nearest  the  car  frame,  arm  C  con- 
nects with  slider  bar  E  which  controls  the  first  speed  and  reverse 
gears.  Moving  the  hand  lever  to  the  rear  gives  the  first  forward 
speed,  and  moving  it  to  the  front  the  reverse.  When  the  hand 
lever  is  in  the  slot  farthest  from  the  car  frame,  arm  C  connects 
with  slider  bar  D,  and  moving  the  lever  forward  gives  the  inter- 
mediate speed,  while  moving  it  backward  gives  the  high  speed  or 
direct  drive.  Arm  F  controls  the  locking  bar  G,  shifting  it  in  the 
direction  of  its  axis  the  same  distance  as  the  tubular  shaft  B  is 
shifted  by  means  of  levers  A.  The  slider  bars  are  provided  with 
a  slot  on  their  under  side  which  allows  the  locking  bar  to  pass 
when  they  are  in  the  neutral  position.  The  locking  bar  has  a  slot 
on  its  upper  side,  and  when  this  slot  is  underneath  a  slider  bar  it 
allows  that  bar  to  be  moved  in  the  direction  of  its  length,  while 
the  other  bar  is  locked  in  position.  A  spring-pressed  ball  engages 
with  conical  holes  in  the  slider  bars,  to  help  the  driver  find  the 
position  of  correct  mesh. 

The  second  type  of  selective  gear  control,  known  as  the  swing- 
ing lever  control,  is  illustrated  in  Fig.  313.  The  control  lever 
is  pivoted  to  a  hub  which  is  free  to  turn  on  the  control  shafts. 
At  the  sides  of  the  control  lever  there  are  two  short  levers, 
which  are  fast  upon  concentric  control  shafts.  Each  of  the  con- 
trol shafts  carries  an  operating  arm  inside  the  frame  member, 
each  operating  arm  being  connected  to  one  of  the  slider  bars. 
The  upwardly  extending  arms  are  provided  at  their  upper 


CONTROL. 


465 


end  with  lugs  bent  at  right  angles,  between  which  lugs  the  con- 
trol lever  engages  when  it  is  pressed  in  the  direction  of  the  par- 
ticular short  lever.  The  control  lever  is  normally  held  in  the 
neutral  position  by  two  flat  springs  secured  to  the  two  short 
levers,  respectively.  Thus,  when  the  control  lever  moves  in  one 
of  the  slots  of  the  quadrant  it  is  connected  to  one  of  the  short 
levers  and  turns  the  control  shaft  to  which  that  short  lever  is 
secured.  Vice  versa,  when  the  control  lever  moves  in  the  other 
slot  of  the  quadrant,  it  operates  the  other  short  lever,  and,  con- 


FIG.  313. — ROCKING  LEVER  SELECTIVE  GEAR  CONTROL. 

sequently  the  control  shaft  to  which  that  lever  is  secured.  The 
slotted  ends  of  the  short  lever  arms  may  extend  right  into  the 
H  quadrant. 

The  third  type  of  gear  control  is  represented  by  the  ball- 
supported  lever  class  of  which  the  Reo,  illustrated  in  Fig.  314, 
was  the  prototype.  This  is  used  exclusively  for  centre  con- 
trol as  the  gear  level  is  mounted  in  a  tubular  projection  cast 
on  the  cover  plate  of  the  gear  housing.  The  lever  has  a  ball 
support  on  two  rings  of  bearing  metal  of  which  the  lower  is 
fitted  against  a  shoulder  in  the  tubular  projection  and  the 


466 


CONTROL. 


CONTROL.  467 

upper  is  held  in  place  by  a  sheet  metal  cap  drawn  down  by 
coiled  springs  anchored  to  the  cover  plate. 

The  lower  end  of  the  lever  is  of  flat  cylindrical  shape  and  is 
adapted  to  engage  into  slots  in  the  sliding  bars  .A  A.  Trans- 
verse holes  are  drilled  through  these  sliding  bars  at  that  part 
where  the  slots  are,  and  each  hole  contains  a  steel  plug  B. 
This  plug  is  reduced  in  diameter  at  the  middle  of  its  length 
and  a  pin  C,  shown  in  dotted  lines,  !s  put  through  the  sliding 
bar  in  such  a  position  that  it  passes  through  the  depression 
of  plug  B  and  prevents  the  latter  from  falling  out  when  the 
sliding  bar  is  handled  separately,  as  in  the  repair  shop.  Lock- 
ing bolts  D  D  are  located  in  bosses  cast  on  the  cover  plate 
and  are  forced  by  coiled  springs  toward  the  sliding  bars.  The 
reduced  inner  end  of  these  locking  bolts  is  of  the  same  dia- 
meter as  the  hole  in  which  the  plug  B  is  located.  With  the 
gear  lever  in  the  central  position,  as  shown,  both  sliding  bars 
are  locked  and  the  lever,  therefore,  cannot  be  moved  in  a  fore- 
and-aft  plane.  If  the  ball  handle  of  the  lever  is  swung  to  the 
right  the  lower  end  of  the  lever  will  force  the  plug  B  entirely 
into  the  left  sliding  bar,  forcing  the  locking  bolt  out  of  it, 
whereupon  the  sliding  bar  may  be  slid  forward  or  backward 
to  engage  the  gears.  Meanwhile  the  right  sliding  bar  is  se- 
curely locked  against  endwise  motion.  It  will  be  noticed  that 
the  shipper  levers  are  screwed  over  the  sliding  bars  for  pur- 
poses of  adjustment. 

While  all  the  different  designs  of  selective  control  may  be 
classed  under  one  of  the  above  heads,  there  are  numerous  vari- 
ations in  detail.  Thus,  the  swinging  lever,  instead  of  being  pivoted 
at  its  end,  may  have  the  pivot  at  some  distance  from  the  end, 
and  the  end  may  be  connected  to  a  sliding  shaft  adapted  to  engage 
with  one  or  the  other  of  the  slider  bars.  In  some  designs  a  con- 
trol lever  is  pulled  by  a  spring  in  the  direction  of  the  outer  slot 
in  the  quadrant,  one  advantage  of  which  is  that  there  is  little 
danger  of  inadvertently  engaging  the  reverse  gear  when  chang- 
ing from  low  to  second,  or  from  high  to  second. 

In  the  past  considerable  trouble  has  been  experienced  in  the 
operation  of  cars  because  of  the  lack  of  uniformity  in  the  ar- 
rangement of  selective  gear  quadrants,  that  is,  the  relative 
arrangement  of  the  different  gear  positions.  This  made  it  awk- 
ward for  a  driver  accustomed  to  one  make  of  car  to  drive 
another  with  the  gear  positions  differently  arranged,  and  even 
involved  an  element  of  danger.  In  order  to  do  away  with  this 
state  of  affairs  the  Society  of  Automobile  Engineers  undertook 


468 


CONTROL. 


FIG.  315.— S.  A.  E.  GEAR  LEVER 
POSITIONS. 


FIG.  316. — REVERSE  SLOT  BLOCK. 


the  work  of  selective  gear  quad- 
rant standardization  and 
evolved  the  preferred  arrange- 
ment shown  in  Fig.  315.  The 
brake  lever  is  usually  pulled  to 
the  rear  in  order  to  apply  the 
brake,  although  there  is  also 
some  variation  from  this  prac- 
tice. 

In  selecting  this  quadrant 
one  point  that  was  kept  in  mind 
was  that  it  is  desirable  to  have 
the  gear  lever  in  the  high  speed 
position  far  removed  from  the 
brake  lever  in  the  off  position, 
so  that  there  is  no  danger  of 
accidentally  getting  hold  of  the 
gear  lever  when  wishing  to 
stop  quickly  in  an  emergency. 
Further,  with  control  levers  in- 
side the  body,  it  is  desirable  to 
have  them  close  together  in  the 
lateral  direction  when  the  gear 
lever  is  in  the  high  gear  posi- 
tion (which  it  is  most  of  the 
time)  so  there  will  be  the  least 
interference  with  lap  robes,  etc. 

Reverse     Lock- Out. — In 

order  to  obviate  the  possibility 
of  accidentally  engaging  the 
reverse  gear,  a  block  is  provided 
which  blocks  the  slot  corre- 
sponding to  the  reverse  until 
after  a  latch  bolt  has  been 
drawn  out  of  place.  Such  a 
block  is  illustrated  in  Fig.  316. 
The  change  gear  lever  is  pro- 
vided with  the  usual  thumb 
button,  which,  however,  is  not 
pressed  as  long  as  the  driver 
wants  to  drive  in  the  forward 
direction.  This  thumb  button 


CONTROL. 


469 


connects  with  a  short  double  armed  lever  pivoted  on  the  side  of 
the  gear  lever,  with  a  down  turned  forward  end  which  abuts 
against  a  raised  portion  on  the  H  quadrant  as  the  gear  lever  is 
about  to  enter  the  reverse  slot.  The  operator  must  then  press  on 
the  thumb  button  before  the  reverse  gear  can  be  engaged. 

Clutch  and  Change  Gear  Interlock — In  order  to  prevent 
shifting  of  the  gears  while  the  clutch  is  engaged,  some  designers 
provide  an  interlock  between  the  gear  sliding  and  clutch  operat- 
ing mechanism.  This  may  be  so  arranged  that  the  gear 
cannot  be  shifted  unless  the  clutch  is  out,  and  the  clutch  can- 
not be  engaged  unless  the  gears  are  in  full  mesh.  Of  course 
the  former  function  is  the  most  important  and  some  interlocks 


FIG.  317. — CLUTCH  AND  GEAR  INTERLOCK. 

are  designed  for  it  alone.  A  diagram  of  one  arrangement  is 
illustrated  in  Fig.  317.  A  sector  is.  secured  to  the  gear  lever 
shaft  and  has  a  slot  across  its  face  parallel  with  the  shaft  into 
which  a  latch  bolt  engages  when  the  gear  lever  is  in  the  neutral 
position.  This  latch  bolt  is  operated  by  means  of  a  linkage  from 
the  clutch  pedal  shaft.  It  will  be  seen  that  with  the  latch  bolt 
in  the  slot  on  the  sector  the  gear  lever  cannot  be  moved  into 
any  of  the  slots  of  the  gate. 

In  pleasure  cars  the  range  of  motion  of  the  brake  lever  handle 
should  not  exceed  16  inches,  and  the  gear  lever  motion  should 
be  less  for  the  sake  of  convenience  in  operation.  Selective  gear 
control  levers  generally  move  only  about  8  inches.  Control  shafts 
and  other  parts  of  a  large  car  should  be  designed  to  have  a 
resisting  moment  of  2,000  pounds-inches,  with  a  stress  of  about 


470 


CONTROL. 


15,000  pounds  per  square  inch  for  low  carbon  steel.  English 
designs  generally  make  their  gear  quadrants  in  the  form  of  a 
box,  the  object  being  to  protect  the  selector  mechanism  and  its 
bearing  from  mud,  etc. 


FIG.  318. — TURNBUCKLE  ADJUSTMENT  FOR  BRAKE  ROD. 

Brake  and  gear  control  shafts  are  generally  arranged  con- 
centrically, though  occasionally  they  are  carried  in  separate  bear- 
ings parallel  and  close  together.  When  arranged  concentrically 
the  brake  control  shaft  is  mostly  the  inner  one,  though  the  reverse 
arrangement  is  also  met  with. 

Brake  Rod  Adjustment. — Fig.  318  shows  a  turnbuckle  ad- 
justment for  brake  rods  which  is  provided  with  a  handy  locking 
device.  The  ends  of  the  two  rods  connected  are  threaded  right 
and  left  respectively.  A  clamp  made  of  sheet  brass  is  hinged 


FIG.  319.— SCREW  ADJUSTMENT  FOR  BRAKE  ROD. 


to  the  buckle  and  its  opposite  end  is  forced  over^a  flattened  por- 
tion of  one  of  the  rods,  thus  preventing  unscrewing  of  the 
turnbuckle.  Another  form  of  adjustment,  seen  particularly  on 
French  cars,  is  shown  in  Fig.  319.  The  rod  is  shown  screwed 
through  the  pivot  pin,  but  it  may  also  be  held  between  two  nuts 
on  opposite  sides  of  the  pin.  It  is  customary  to  make  the 
diameter  of  the  trunnion  equal  to  twice  the  diameter  of  the  rod. 


CHAPTER  XVII. 


THE  FRAME  AND   ITS   BRACKETS. 

Automobile  frames  are  almost  exclusively  made  of  pressings 
from  sheet  steel.  Laminated  wood  and  armored  wood  frames 
are  used  by  a  few  manufacturers  of  pleasure  cars,  and  rolled 
section  steel  frames  by  some  makers  of  commercial  cars. 

Materials. — Originally  pressed  steel  frame  members  were 
made  of  cold  rolled  Bessemer  steel,  with  a  carbon  content  of 
about  0.10  per  cent.  Bessemer  steel  has  since  been  discarded 
in  favor  of  open  hearth  steel,  and  while  cold  rolled  sheets  are 
still  used  in  most  cases,  hot  rolled  stock  has  also  come  into 
use.  Frames  are  also  made  of  chrome-nickel  steel.  Alloy 
steel  frames  are  now  always  heat  treated,  it  having  been  found 
that  without  heat  treatment  the  gain  in  elastic  limit  hardly  war- 
rants trie  additional  cost  of  the  special  steel. 

The  most  widely  used  frame  material  at  the  present  time 
is  open  hearth  carbon  steel  of  about  0.20  per  cent,  carbon 
content.  In  the  annealed  condition  such  steel  has  an  elastic 
limit  of  about  35,000  pounds  per  square  inch.  Steel  with  a 
somewhat  higher  carbon  content,  about  0.25  per  cent.,  is  also 
used,  and  has  a  somewhat  higher  elastic  limit,  but  is  not  as 
malleable  as  the  low  carbon  product.  The  chief  reason  for 
using  cold  rolled  steel  is  because  of  the  natural  bright  finish  of 
this  steel  as  it  comes  from  the  mill. 

On  page  473  are  given  the  physical  properties  of  three  steels 
recommended  for  use  in  pressed  steel  frames  by  the  Society  of 
Automobile  Engineers.  Two  of  these  are  carbon  steels  and  the 
third  is  an  alloy  steel. 

Sheet  steel  for  frames  is  measured  by  the  United  States 
sheet  metal  gauge,  and  is  furnished  in  thicknesses  of  0.125,  0.156, 
0.187  and  0.250  inch. 

Frame  Sections. — The  side  rails  of  automobile  pressed  steel 
frames  are  invariably  made  of  channel  section,  with  the  open 

471 


472 


THE  FRAME  AND  ITS  BRACKETS. 


vx\ 


CQ 


THE  FRAME  AND  ITS  BRACKETS. 


473 


side  turned  inward.  Most  of  the  cross  members  employed  are 
also  of  channel  section.  The  side  rails  are  the  most  important 
parts,  they  being  subjected  to  the  greatest  unit  stress  and  con- 
stituting the  bulk  of  the  weight.  The  height  of  the  section 
is  constant  over  a  certain  portion  at  the  middle  of  the  rails, 
generally  about  one-third  the  whole  length,  and  decreases 
uniformly  toward  both  ends.  Straight  side  rails  are  by  far 
the  cheapest  to  produce,  and  are  generally  used  for  low  priced 
cars,  but  in  the  larger  size  vehicles  it  is  necessary  to  narrow  the 
frame  in  front  in  order  to  enable  the  car  to  turn  in  a  circle  of 
reasonably  small  radius,  and  to  give  it  a  single  or  double  drop,  or 
a  "kick  up"  over  the  rear  axle,  in  order  to  bring  the  centre  of 
gravity  down  low  without  inordinately  reducing  the  clearance 
between  the  frame  and  axles  required  for  proper  spring  action. 

S.  A.  E.  FRAME  STEELS. 

Chemical  and  physical  properties  recommended  as  embody- 
ing current  practice  minima: 


Chemical 

Elastic 
Limit,  Lbs. 
Per  Sq.  In. 

Reduction 
of  Area, 
per  cent. 

Elongation 
in  2" 
per  cent. 

S.  A.  E.  Steel 
1020 
Carbon  Steel 
(.15-.25  Carbon) 

Natural 

35,000 

45 

25 

•*.  A.  E.  Steel 
1025 
Carbon  Steel 
(.20.30  Carbon) 

Heat 
Treated  Natural 

40,000 

45 

20 

60,000 

50 

20 

S.  A.  E.  Steel 
3230 
Nickel  Chromium 
(.25-.3S  Carbon) 

Heat 
Treated 

85,000 

50 

18 

Insweep  and  Drop. — The  insweep  of  the  frame  at  the  front, 
to  reduce  the  turning  radius,  confronts  designers  with  a  diffi- 
cult problem,  as  it  imposes  a  twisting  moment  on  the  frame 
bar  at  the  bend,  and  a  light  channel  section  has  very  little  re- 
sistance to  twisting  strains. 


474 


THE  FRAME  AND  ITS  BRACKETS. 


When  pressed  steel  frames  narrowed  in  front  were  first  used 
the  "insweep"  was  generally  in  the  form  of  a  compound  curve 
of  very  short  radius.  This  greatly  weakened  the  frame  and  often 
led  to  trouble.  At  present  it  is  customary  to  extend  the  insweep 
over  a  great  length  and  to  increase  the  width  of  the  flanges 
at  the  frame.  Several  designs  of  frame  bars  inswept  in  front 
are  shown  in  Fig.  319A.  In  design  A  the  inner  edge  of  the  flange 
runs  parallel  with  the  longitudinal  axis  of  the  car  up  to  the  end  of 
the  offset,  whence  it  runs  in  a  straight  line  to  the  rear  end,  where 
the  flange  is  made  as  wide  as  at  the  front  end.  In  design  7? 
the  inner  edge  of  the  flange  runs  parallel  with  the  car  axis  to  a 
point  just  beyond  the  intermediate  cross  member,  beyond  which 
the  flange  is  of  the  same  width  as  in  front.  In  design  C  the 
flanges  are  widened  only  at  the  offset. 


FIG.  321. — INSWEPT  FRAME  REINFORCED. 


Fig.  320  shows  side  views  of  four  types  of  side  rails,  A 
being  the  ordinary  straight  rail ;  B,  a  rail  with  a  single  drop ; 
C,  a  rail  with  double  drop,  and  D,  a  rail  with  a  kick-up  over  the 
back  axle. 

The  greatest  offset  in  the  front  part  of  the  frame  side  rails 
is  probably  required  in  taxicabs,  whose  frame  must  be  very 
narrow  in  front  in  order  to  admit  of  turning  around  in  an 
ordinary  city  street  without  backing,  and  comparatively  wide 
in  the  rear  so  the  rear  seat  will  accommodate  three  passengers 
without  crowding,  This  problem  is  sometimes  solved  by 


THE  FRAME  AND  ITS  BRACKETS.  475 

using  channel  section  reinforcements  in  the  side  bars  at  the 
front  end,  which  extend  to  a  cross  member  somewhat  to  the 
rear  of  the  bend  in  the  frame,  as  shown  in  Fig.  321. 

To  obviate  the  weakening  effect  of  offset  rails  and  still  have 
the  frame  narrow  in*  front  the  side  rails  may  be  made  straight  and 
set  so  as  to  approach  each  other  toward  the  front. 

Calculation  of  Side  Rail  Section— Each  frame  side  rail  con- 
stitutes a  beam  which  is  supported  at  four  points,  the  points 
of  spring  attachment,  as  oiiown  in  Fig.  322.  The  reactions  R 
at  opposite  ends  of  each  spring  will  be  equal,  and  the  re- 
sultant of  these  two  reactions  acts  on  the  frame  midway  be- 
tween spring  eyes  or  directly  above  the  axle.  In  a  pleasure 
car  of  standard  design  the  weight  on  the  frame  is  distributed 
more  or  less  uniformly  from  a  point  substantially  above  the 
front  axle  to  a  point  a  little  behind  the  rear  axle,  and,  there- 
fore, we  will  not  be  far  wrong  in  considering  the  frame  side 
bar  a  beam  supported  at  two  points,  directly  above  the  axles, 

A  A  A  A  i  i  1  II  .  til  1  11  1  1  1  1  1  n  1  l  11 


2*  2R, 

FIG.  322. — DIAGRAM  OF  LOAD  AND  REACTIONS  ON  FRAME  RAIL. 

and  carrying  a  uniformly  distributed  load  between  points  of 
support. 

Let  /  =  the  distance  beween  supports  (wheelbase),  and  W 
the  weight  carried  by  each  frame  rail,  then  the  maximum 
bending  moment,  which  occurs  midway  between  supports,  is 

— .      It    is    evident   that   the    modulus    of    the    section    at    the 

point  of  maximum  bending  moment  should  be  proportional 
to  this  moment.    Calling  the  necessary  factor  of  safety  /,  then 
Wl     ZZ 
8    =  f, 

where  Z  is  the  section  modulus  and  L  the  elastic  limit  of  the 
material.  Just  what  value  should  be  given  to  /  cannot  well 
he  determined  from  first  principles.  The  above  equation  may 
be  transposed  to  read 

z-WJLL 

-    8Z 
The  weight  W  on  one  frame  rail  is  proportional  to  the  total 


476  THE  FRAME  AND  ITS  BRACKETS. 

weight  of  the  car  with  load  (Wi).    Hence  we  may  write 
_  a  W^lf        laf\  W^  I 
8  L        =  \TJ    L 

Denoting  the  expression  (  —  )  by  c  we  have 

W*l 

Z=c    £ 

In  frames  for  pleasure  cars  built  up  to  1910  the  average  value 
of  c  was  0.12.  However,  when  the  fore-door  type  of  body  came 
into  use  considerable  trouble  was  experienced  from  cramping  ol 
the  front  doors.  These  are  located  not  far  from  midway  be- 
tween the  points  of  support  of  the  frame,  where  the  deflection 
is  the  maximum.  To  obviate  this  cramping,  the  constant  r  is 
now  made  equal  to  about  0.16  for  carbon  steel  and  as  high  as 
j.2o  for  alloy  steel,  in  the  case  of  high  powered  cars.  For  low 
powered  cars,  especially  those  of  short  wheelbase,  like  20-25 
ftotse  power  runabouts,  a  frame  rail  whose  section  modulus  gives 
a  value  of  0.10-0.12  to  the  constant  c  is  amply  strong.  Therefore, 
to  sum  up  for  pleasure  cars : 

Z^C^i (74) 

J^f 

c  =  0.10-0.12  for  low  powered  small  cars; 

c  =  o.i6  for  high  powered  cars  with  carbon  steel  frames; 

c  =  0.2,0  for  high  powered  cars  with  alloy  steel  frames. 

The  fore-door  body  has  made  stiffness  of.  the  frame  an  im- 
portant factor,  and  from  this  point  of  view  the  use  of  alloy  steel 
offers  little  advantage. 

In  the  above  the  frame  rails  have  been  considered  as  simple 
beams  subjected  to  bending  stresses  and  shear  only.  As  a  mat- 
ter of  fact,  the  rear  springs  usually  are  located  outside  the  frame 
-ind  the  reaction  at  their  points  of  attachment  imposes  a  tor- 
sional  stress  on  the  side  rails.  However,  very  little  torsion  oc- 
curs, because  the  cross  members  take  up  these  stresses.  With 
the  usual  three-quarter  elliptic  rear  springs  the  quarter  eli^tx 
members  are  often  bolted  directly  to  extensions  of  the  rear 
cross  member,  and  only  the  reaction  at  the  forward  spring 
shackle  can  produce  trosion  in  the  side  rail.  It,  therefore,  is  not 
essential  to  consider  the  torsional  moment  of  outside  springs  in 
the  calculation  of  the  frame  section,  but  cross  members  should 
preferably  be  placed  as  close  to  the  point  of  spring  attachment  to 
the  frame  as  possible. 

In  motor  trucks  the  bending  moment  on  the  frame  rails  fol- 
lows a  somewhat  different  curve,  for  the  reason  that  usually  the 


THE  FRAME  AND  ITS  BRACKETS. 


477 


load  considerably  overhangs  the  rear  axle.  C.  F.  Cleaver  in  the 
Automobile  Engineer  of  August,  1912,  published  a  diagram  of 
bending  moments  and  shear  in  the  frame  of  a  4  ton  truck  of 
standard  design,  which  diagram  is  herewith  reproduced  (Fig. 
323).  Of  course,  the  weights  of  the  individual  parts  of  the 
mechanism  are  generally  not  accurately  known  when  the  frame 
is  designed,  and  sufficiently  close  results  will  be  obtained  by  as- 
suming the  total  weight  of  truck  and  load  and  using  a  formula 
of  the  same  form  as  (74)  but  with  a  different  coefficient,  be- 
cause of  the  different  weight  distribution,  speed  and  type  of  tires, 
as  compared  with  pleasure  vehicles.  Commercial  vehicle  data 


nding  Moment 


FIG.  323. — DIAGRAM  OF  BENDING  MOMENTS  AND  SHEARING  FORCE 
ON  MOTOR  TRUCK  FRAME  RAIL. 

in  the  author's  possession  shows  that  in  average  modern  practice 

W\l 

Z  =  o.og  —jT- « (75) 

This  equation  is  to  be  used  only  if  the  load  overhangs  the  rear 
axle  as  much  as  in  Fig.  323.  If  the  overhang  is  much  less  a 
somewhat  greater  coefficient  should  be  used. 

The  Society  of  Automobile  Engineers  has  been  endeavoring 
to  standardize  pleasure  car  frames  and  recommends  the  fol- 
lowing practice: 


478  THE  FRAME  AND  ITS  BRACKETS. 


j 

-4 


t 


FIG.  324. — FRAME  MEMBERS. 

A — Amount  of  drop  between  top  of  side  rail  and  front  spring 
bolt: 

4"  or  4%"  drop  for  3"  side  rail 
4%"  or  5"  drop  for  3%"  side  rail 
5"  or  Sy2"  drop  for  4"  side  rail 
5%"  or  6"  drop  for  4%"  side  rail 
6"  or  6%"' drop  for  5"  side  rail 
6%"  or  7"  drop  for  5&"  side  rail 
7"  -or  7%"  drop  for  6"  side  rail 

B — Represents  radius  of  curve  of  bottom  flange  of  side  rail 
at  front  end: 

8",  12",  16",  20"  and  24" 

C — Rear-end  rise — amount  of  difference  between  level  of 
frame  at  rear  and  top  flange  of  side  member: 

2",  3",  4"  and  5" 

D — Radii  of  combined  curve  in  bottom  flange  .of  side  mem- 
ber to  make  rise  at  C: 

10",  20"  and  30" 

E — Side  rail  offset  to  commence  at  least  10"  back  of  rear 
end  of  front  end  taper. 

CROSS   MEMBERS 

F — Recommended  widths  of  gusset  plate  ends — 4",  5"  and  6". 
G — Radii  of  curved  gusset  plates  to  be  3"  and  4".     Straight 
gusset  plates  to  be  cut  at  angle  of  45°. 

Members  with  straight  drops  could  be  made  to  have  drops 
vary  in  multiples  of  %",  adopting  a  constant  angle  for  the 
dropped  portion. 

H — Top  of  subframe  to  be  on  line  with  inner  side  of  lower 
flange  of  side  rail. 

I — width   between   bars   for  flywheel   clearance   to   be   17", 

and  18". 
J— Recommended  width  of  all  engine  bar  flanges  to  be  iy2". 


THE  FRAME  AND  ITS  BRACKETS.  A. 

WIDTH   OF  FRAME 

30"  for  front  end  of  frame,  the  width  in  rear  to  vary  with 
side  rail  offset. 

Hot  Riveting 

Diameter  Spacing  Distance 

Diameter  of  Rivet  Drilled  Hole  Between  Centres 

5/16"  11/32"  1%" 

3/8"  13/32"  iy2" 

RADIUS   OF    FILLETS 

3/16"   for   sections   below   5" 
^4  for  sections  5"  and  above. 

MISCELLANEOUS 

Length  of  straight  centre  sections  of  side  rails  to  be  designed 
in  multiples  of  2". 

Taper  of  side  rail  ends  to  be  1/16"  to  1".  This  taper  coin- 
cident with  centre  sections  in  multiples  of  2",  will  produce  a 
depth  of  section  at  extreme  ends  of  side  rails  varying  in  mul- 
tiples of  %". 

TABLE  IX— SIDE  RAIL  SECTIONS. 


C. 

A. 

B. 

Variable 

Outside 

Dimension. 

Desig- 

Flange 

Punch 

Using 

Using 

Using 

Using 

nation. 

Width. 

Size. 

o.  125 

o.  156 

0.187 

0.250 

!n. 

In. 

In. 

In. 

In. 

In. 

In. 

3 

1  54 

254 

3 

3     1-16 

3/2 

1/2 

3/4 

3/2 

3    9-i6 

35A 

4 

I}4 

3  11-16 

3  15-16 

4 

41-16 

4  3-  it 

4/4 

1/4 

4H 

4^6 

4     7-i6 

4% 

4H 

5 

I& 

4H 

4^ 

4  15-16 

5 

5/8 

5/2 

iM 

S% 

5^ 

5     7-i6 

5/4 

55/8 

6 

Iti 

sH 

S7/s 

5  15-16 

6 

6Ji 

This  completes  the  specifications  of  side  rails.  It  will  be  ob- 
served  that  standardization  of  this  part  has  been  carried  farther 
than  that  of  almost  any  other  automobile  part.  Makers  of  auto- 
mobile frames  took  an  active  interest  in  this  work  of  stand- 
ardization, as  it  enables  them  to  turn  out  a  great  range  of 
frames  with  a  minimum  investment  in  dies. 


480 


THE  FRAME  AND  ITS  BRACKETS. 


Following  are  the  section  moduli  of  these  sections: 

TABLE  X— SECTION  MODULI  OF    FRAME    SECTIONS. 


B. 

3.000 
3.5oo 
3.062 
3-9375 

4-375 
3-625 
4.000 
4.062 
4-437 


4.375 
4.500 
5-375 
4.937 
4.187 
5.875 
5-437 
4.625 
5.000 
5-937 
5-500 
6.000 
5.125 
5.625 
6. 125 


C. 

•  5 
•5 

•  5 

•  5 
•5 
-5 
-5 
-5 
•5 
•5 
-75 
•5 
•75 
•75 

•  5 
•75 
•75 

•  5 

•  75 

•  75 
•75 
•7.5 
•75 
•75 
•75 


0.125 
0.125 
0.156 
0.125 
0.155 
0.125 
0.187 
0.156 
o.  187 
o.  156 
0.125 
0.187 
0.125 
0.156 
0.250 
0.125 
0.156 
0.250 
0.187 
0.156 
0.187 
0.187 

0.250 
0.250 
0.250 


Z. 

0.66 
0.81 
0.86 
0.98 
i.  08 


1.18 
1.26 
1.40 
1.47 
1-53 
1.56 
1.67 
1.84 
1.87 
.1.90 
2.06 
2.16 
2.17 
2.19 
2.45 
2.78 
2.86. 
3-26 
3-70 


Following  are  the  dimensions  and  constants  of  standard  rolled 
steel  channels  sometimes  used  for  truck  frames : 

TABLE  XI— PROPERTIES  OF  ROLLED  CHANNELS. 


Depth. 
5     •  •  • 

Thickness 
of  Web. 

O.IQ 

Width 

of  Flange. 
i  .  75 

Weight 
Per  Foot 
(Pounds). 
6.5 

Moment 
of 
Inertia. 

Section 

Modulus. 

i    89 

8  o 

6     . 

o.  20 

i  .  92 

g 

6 

6    . 

O    44 

2    l6 

?  8 

7     ... 

0.21 

2.09 

9  •  75 

60 

6  o 

7 

,  .     O.44 

2.  3O 

I4  75 

78 

g 

2    26 

8 

2  is 

6't-  5 

8    . 

.  .     O.4O 

2.AA 

16.2* 

7Q  .O 

TO.O 

The  moment  of  inertia  and  section  modulus  as  given  in  the 
above  table  apply  to  a  neutral  axis  perpendicular  to  the  web  at 
the  centre. 

Cross  Members. — Cross  members  are  made  of  widely  different 
forms,  according  to  the  parts  they  have  to  support,  etc.  At  the 
ends  they  are  made  of  an  outside  height  equal  to  the  inside  height 
of  the  side  rail  section  at  that  particular  point,  so  as  to  fit  into 
the  side  rail  channel.  In  pleasure  car  frames  there  are  usually 


THE  FRAME  AND  ITS  BRACKETS. 


481 


four  cross  members,  one  in  front,  one  at  the  rear  and  two  inter- 
mediate ones,  though  if  a  sub-frame  is  used  there  is  generally 
only  one  intermediate  cross  member,  back  of  the  change  gear 
box.  The  front  cross  member  usually  comes  underneath  the 
radiator,  being  dropped  to  accommodate  the  latter,  and  also  car- 
ries the  bracket  for  the  starting  crank.  The  two  intermediate 
cross  members  generally  support  the  change  gear  and  they  often 
have  to  be  dropped  to  pass  underneath  the  gear  box  or  the  drive 
shaft,  arched  to  pass  over  the  top  of  the  box  or  shaft  or  made  of 


FIG.  325. — REAR  GUSSET. 

comparatively  large  height  at  the  middle  and  with  a  hole  through 
which  the  drive  shaft  passes.  The  rear  cross  member  can  gen- 
erally be  made  straight,  and  it  is  customary  to  use  a  specially  large 
gusset  at  the  rear  corner  of  the  frame  in  order  to  prevent  any 
tendency  to  distortion.  A  popular  design  of  rear  corner  gusset  is 
shown  in  Fig.  325.  In  England  tubular  cross  members  are  used 
to  quite  an  extent,  and  cross  members  of  cast  steel  and  man- 
ganese bronze  are  also  in  use. 

Sub=frames — Sub-frames  on  which  the  engine  and  change 
gear  are  supported  are  still  used  to  a  considerable  extent,  al- 
though not  as  much  as  formerly.  These,  too,  are  generally  made 
of  channel  section  pressed  steel,  and  are  riveted  to  the  forward 
and  an  intermediate  cross  member,  being  so  placed  that  the  top 
of  the  sub-frame  comes  flush  with  the  inner  side  of  the  lower 
flange  of  the  main  frame  rail.  A  typical  sub-frame  construction 
is  shown  in  Fig.  326. 

In  designing  drop  bars,  the  radii  of  the  outlines  should  be  made 
as  large  as  possible,  as  short  curves  are  hard  to  draw.  The  width 
of  the  flanges  should  be  made  equal,  or  at  least  nearly  so,  and  the 
ends  of  the  bar  should  preferably  be  so  designed  that  the  flanges 


-'.32      THE  FRAME  AND  ITS  BRACKETS. 

are  trimmed  to  the  same  length.     Stock  will  be  economized  if  an 
integral  gusset  is  provided  for  on  the  lower  flange. 

Frame  Joints — The  individual  parts  of  pressed  steel  frames 
are  joined  by  riveting,  either  separate  or  integral  gussets  being 
used  (A  and  B,  Fig.  327).  Two  methods  of  riveting  are  in  use, 
viz.,  cold  riveting  and  hot  riveting.  In  testing  a  hot  riveted  joint 
under  tension  in  the  plane  of  contact,  as  the  tension  assumes  a 
certain  definite  value,  there  is  a  sudden  increase  in  extension. 
This  is  due  to  the  fact  that  up  to  this  point  the  tension  is  re- 
sisted by  the  contact  friction  which  in  a  hot  riveted  joint  is  very 


O 


O 


o 

— 


n 


FIG.  326. — SUB-FRAME  CONSTRUCTION. 


considerable,  because  the -rivet  in  cooling  draws  the  two  parts  to- 
gether with  great  force,  and  to  the  further  fact  that  the  rivet,  also 
because  of  its  contraction  in  cooling,  does  not  entirely  fill  up  the 
hole.  With  cold  riveting  the  hole  is  completely  filled  by  the 
rivet,  but,  on  the  other  harid,  the  surfaces  are  not  applied  to  each 
other  with  as  great  force.  It  seems  that  hot  riveting,  on  the 
whole,  has  proven  the  most  satisfactory  and  is  now  in  general 
use.  Two  sizes  of  rivets  are  used,  1%  and  ^  inch.  The  holes 
for  hot  riveting  for  these  two  sizes  are  made  M  and  £|  inch, 
respectively,  and  are  spaced  about  il/2  inches.  In  riveting 
brackets  to  frame  members,  three  rivets  are  often  used.  All 
rivet  holes  weaken  the  frame,  but  the  weakening  effect  varies 
greatly  with  the  location  of  the  holes.  A  hole  at  the  middle  of 
the  web  has  but  little  effect,  but  the  opposite  is  true  of  a  hole 
in  one  of  the  flanges.  In  this  connection  it  is  well  to  remember 
that  the  lower  flange  is  under  tension  and  the  upper  under  com- 


THE  FRAME  AND  ITS  BRACKETS. 


483 


pression,  the  unit  stress  being  the  same  in  both,  and  since  the 
compressive  strength  of  frame  materials  is  somewhat  greater 
than  their  tensile  strength,  it  is  advisable  to  put  rivet  holes  in  the 
upper  rather  than  in  the  lower  flange,  where  this  can  be  done 
just  as  well. 

At  the  New  York  automobile  show  in  1906  the  Darracq  Auto- 
mobile Company  of  France  exhibited  a  complete  sheet  metal 
frame  in  one  piece  which  aroused  a  great  deal  of  curiosity  at  the 
time.  It  was  undoubtedly  made  from  separate  stampings  by 
means  of  the  oxy-acetylene  welding  process  which  was  then 


FIG.  327— TYPES  OF  GUSSET  PLATES. 


in  its  infancy.  The  frame  was  highly  polished  and  showed  abso- 
lutely no  evidences  of  joints.  While  it  is  quite  possible  to  make 
rivetless  frames  in  this  way  the  advantages  secured  do  not  war- 
rant the  cost.  In  fact,  a  well  made  riveted  pressed  steel  frame, 
of  ample  section  for  the  load  to  be  carried  lasts  well  and  gener- 
ally gives  very  little  trouble. 

Underslung  Frames — An  underslung  frame — that  is,  a  frame 
located  underneath  the  axles — is  sometimes  used  because  of  the 
low  centre  of  gravity  it  gives.  By  means  of  a  raised  sub-frame 
the  engine  and  gear  box  are  placed  at  about  the  same  distance 
from  the  ground  as  ordinarily,  because  to  lower  them  would 
mean  reducing  the  ground  clearance;  but  the  frame,  body  and 
passengers  are  materially  lowered,  which  lowers  the  centre  of 
gravity  of  the  whole  car  and  increases  its  stability.  Specially 
large  wheels  are  employed  in  connection  with  underslung  frames, 
which  increases  the  ground  clearance  and  incidentally  tends  to 
give  a  straight  line  drive.  The  frame  is  usually  the  lowest  part 
of  the  car  and  has  a  ground  clearance  of  9  to  10  inches. 


484 


THE  FRAME  AND  ITS  BRACKETS. 


FIG.  328. — UNDERSLUNG  FRAME  RAIL. 

Fig.  328  shows  the  general  form  of  the  side  rail  of  an  underslung 
frame. 

Wood  Sill  Frame. — The  H.  H.  Franklin  Manufacturing  Com- 
pany uses  a  frame  made  of  wood  sills.  Each  sill  is  made  of  three 
laminae  of  second  growth  white  ash,  which  has  been  air  sea- 
soned and  kiln  dried  in  the  plank,  the  laminae  being  glued  and 
screwed  together,  and  so  arranged  that  the  grain  in  adjacent  ones 
runs  at  a  slightly  different  angle.  The  built-up  sill  is  kiln  dried 
at  a  somewhat  lower  temperature  than  the  lumber,  and  is  then 
shaped  to  the  exact  size  required.  Thin  strips  are  then  glued 
along  the  top  and  bottom  edges  to  cover  the 
joints  in  the  main  portion  of  the  sills,  so  as 
to  keep  out  moisture.  Next,  two  side  sills 
are  placed  in  their  proper  relation  to  each 
other  and  connected  by  cross-pieces.  The 
rear  corners  are  metal  bound  and  provided 
with  4  inch  gusset  blocks.  The  attachment 
of  brackets,  painting  and  varnishing  complete 
the  frame. 

A  wood  sill  of  selected  material  and  prop- 
erly  proportioned    is    stronger   in    a   vertical 
plane  than  a  steel   frame  rail  of  the  usual 
proportions  and  of  equal  weight.     Thus,  ac- 
cording to  tests  made  by  the  engineers  of  the 
Franklin  Company,  a  pressed  steel  side  rail 
having  a  section  of  4^x1  ^xfs  inch,  and  a 
FIG.  329. — SECTION    weight  per  linear  inch  of  0.408  pound,  has  a 
OF     FRANKLIN       resisting  moment   of    114,830  pounds-inches, 
WOOD   SILL.  whereas  an  ash  sill  measuring  124x6  inches 

and  weighing  0.266  pound  per  linear  inch 
has  a  resisting  moment  of  142,275  pounds-inches.  That  wood  sill 
frames  are  not  more  generally  used  is  probably  due  to  the  diffi- 
culty of  securing  really  faultless  wood  and  to  the  very  careful 
handling  the  wood  requires  in  the  process  of  manufacture,  which 
makes  the  frame  rather  expensive.  Besides  lightness,  it  is 
claimed  for  the  wood  sill  frame  that  it  absorbs  shocks  and  muffles 
noise. 


THE  FRAME  AND  ITS  BRACKETS. 


-.00 


Wood  sills  reinforced  with  steel  flitch  plates  and  square  tubes 
filled  with  wood  have  also  been  used,  especially  abroad,  but  have 
been  practically  entirely  discarded  in  favor  of  pressed  steel. 

Frame  Trusses— Frame  trusses  in  the  past  frequently  were 
used  as  last  resorts  in  cases  where  the  frame  was  found  to  be  too 
light  for  the  load  after  the  car  had  been  built.  It  may  be  that 
this  brought  them  into  disrepute,  for  at  present  they  are  prac- 
tically never  used  on  pleasure  cars  and  only  on  a  few  motor 
trucks.  The  use  of  trusses  in  railway  cars  is  universal,  and  their 
use  on  motor  trucks  should  permit  of  a  considerable  saving  on 
the  weight  of  the  frame.  The  only  objection  that  can  be  raised 
to  a  properly  designed  truss  is,  that  if  it  should  be  improperly 
adjusted  by  an  incompetent  driver  it  would  give  trouble.  Trusses 
are  known  as  two  panel  or  three  panel,  according  to  whether 
one  or  two  struts  are  used.  With  a  two  panel  truss  the  strut  is 
preferably  located  midway  between  anchorages,  and  with  a  three 
panel  truss  the  distance  between  anchorages  should  be  divided 
into  three  equal  parts  by  the  struts.  Probably  the  chief  reason 
that  trusses  are  now  seldom  used  on  motor  trucks  is  that  the 
bodies  of  these  trucks  usually  overhang  the  rear  axles  to  such  an 
extent  that  the  bending  stress  in  the  fidme  directly  over  the  rear 
axle  is  as  great  as  at  the  point  of  maximum  bending  moment  be- 
tween axles.  Trusses,-  of  course,  are  of  particular  value  in 
vehicles  of  very  long  wheel  base  and  with  comparatively  little 
overhang.  The  best  anchorage  points  are  the  points  at  which 
there  is  no  bending  moment,  which  is  some  distance  inside  the 
axles. 

The  tension  in  the  truss  rod  and  the  compression  in  the^strut 
can  be  easily  calculated.  Suppose  that  the  load  on  the  frame  be- 
tween the  points  of  anchorage  is  evenly  distributed  and  that  the 
truss  is  so  adjusted  that  it  relieves  the  frame  at  the  point  where 
the  strut  is  secured  to  it  of  all  bending  stress.  Then  (Fig.  330) 
calling  the  total  weight  on  the  frame  between  truss  anchorage  W, 
the  compression  on  the  strut  is  W/2  and  the  tension  in  each  truss 
rod  is  W/(4  sin  a).  Since  the  load  on  the  truss  is  a  dynamic  one, 


FIG.  330.— DIAGRAM  OF  FRAME  TRUSS. 


486 


THE  FRAME  AND  ITS  BRACKETS. 


a  safety  factor  of  at  least  4  should  be 
allowed  in  both  the  truss  rod  and  the  strut. 
The  stress  on  the  strut  depends  merely 
upon  the  weight  carried  by  the  frame,  but 
the  tension  in  the  rods  is  less  the  greater 
the  height  of  the  strut  or  struts  and  the 
shorter  the  length  of  the  end  panels. 

Some  means  of  adjustment  must  be  pro- 
vided. Either  the  ends  of  the  truss  rods 
may  be  threaded  and  provided  with  nuts; 
a  turnbuckle  may  be  inserted  in  one-half 
of  the  truss  rod,  or  the  strut  may  be  so  ar- 
ranged that  it  can  be  lengthened  or  short- 
ened. Fig.  331  illustrates  a  design  of 
trussed  frame  for  a  motor  truck. 

Spring  Brackets — The  chassis  frame  is 
carried  on  the  springs  through  the  in- 
termediary of  spring  brackets.  At  the 
front  semi-elliptic  springs  are  used,  as  a 
rule,  which  require  a  bracket  at  either 
end.  The  forward  bracket  is  generally 
made  in  the  form  shown  in  Fig.  332.  It 
tits  into  the  downwardly  curved  forward 
end  of  the  frame  channel  to  which  it  is  se- 
cured by  one  rivet  in  the  vertical  plane  at 
the  extreme  forward  end  of  the  channel, 
and  three  or  more  horizontal  rivets.  In 
the  cheaper  cars  and  in  commercial  vehi- 
cles this  bracket  is  usually  made  in  the 
form  of  a  plain  forked  connector,  but  in 
the  design  illustrated  the  spring  eye  is 
surrounded  by  a  shroud  which  extends  a 
little  below  the  axis  of  the  spring  bolt  and 
completely  encloses  the  spring  eye.  This 
makes  for  a  neater  appearance  than  an  open 
forked  bracket.  The  eye  bolt  can  be  held 
from  rotating  in  the  bracket  either  by  a 
small  pin  extending  into  its  head  from 
underneath  and  into  the  prong  of  the  fork, 
or  by  a  small  key. 

The  rear  ends  of  semi-elliptic  front 
springs  are  connected  to  the  frame  brackets 
by  shackles,  and  these  shackles  may  work 


THE  FRAME  AND  ITS  BRACKETS.  43? 


FIG.  332. — FRONT  SPRING  FRONT  BRACKET. 

either  under  compression  or  under  tension,  the  brackets  being 
designed  accordingly.  Simplicity  of  construction  is  in  favor  of 
shackles  under  compression,  and  these  are  now  generally  used, 
even  on  the  most  expensive  cars.  Fig.  333  shows  two  forms  of 
front  spring  rear  brackets  for  shackles  working  under  compres- 
sion. That  shown  at  A  does  not  require  any  rivets  through  the 
flange  of  the  frame  rail,  and  therefore  may  be  considered  the 
better  construction,  although  at  this  point  of  the  frame  rail  the 
strain  on  the  material  usually  is  not  very  great. 

The  rear  springs  at  their  front  end  are  either  pivoted  or 
shackled  to  their  brackets.  Two  designs  of  brackets  for  this  part 
of  the  car  are  illustrated  in  Fig.  334.  The  one  shown  at  A  is  a 
plain  fork  and  is  secured  to  the  frame  by  three  rivets,  one  of 
which  passes  through  the  lower  flange.  The  design  shown  at  B 
is  of  the  shrouded  type,  which  gives  a  somewhat  neater  appear- 
ance if  the  front  end  of  the  rear  spring  is  exposed  to  view. 


FIG.  333.— FRONT  SPRING  REAR  BRACKETS. 


488 


THE  FRAME  AND  ITS  BRACKETS. 


Generally,  however,  it  is  covered  with  a  shield,  and  an  open  type 
of  bracket  is  used. 

The  bracket  for  the  rear  spring  front  end  is  sometimes  com- 
bined with  a  bearing  for  the  brake  shaft  and  also  with  a  bracket 
for  the  forward  end  of  the  radius  rod.  For  instance,  the  bracket 
may  be  made  with  a  follow  stud  surrounded  by  the  hub  part  of  a 
shackle  forging,  and  the  brake  shaft  extend  through  the  hollow 
stud. 

If  semi-elliptic  springs  are  used  at  the  rear  the  frame  rail 
may  be  curved  downwardly,  the  same  as  in  front,  and  provided 


°) 


_^— J 


FIG.  334. — REAR  SPRING  FRONT  BRACKETS. 

with  a  bracket  similar  to  that  shown  in  Fig.  332.  A  bar  is  then 
run  through  the  eyes  of  the  bracket  on  opposite  sides  of  the 
frame,  whose  ends,  somewhat  reduced  in  diameter,  serve  as  the 
spring  shackle  bolts.  This  practice  is  more  or  less  prevalent  in 
Europe.  An  alternate  construction  consists  in  the  use  of  long 
spring  brackets  of  the  general  form  shown  in  Fig.  335  at  A. 
Brackets  of  this  type  are  riveted  to  the  bottom  flanges  of  the 
side  rail  and  rear  cross  member  and  also  to  the  web  of  the  latter. 
The  short  members  of  three-quarter  elliptic  springs  may  be 
secured  by  bolts  or  clips  to  brackets  riveted  to  the  side  rails  near 
their  rear  ends,  or  may  be  clamped  between  extensions  of  the 
flanges  of  the  rear  cross  member,  as  illustrated  in  Fig.  335  at  B. 
In  the  design  shown  the  spring  plate  has  three  holes  drilled 
through  it,  the  forward  one  of  which  is  for  the  usual  spring 


THE  FRAME  AND  ITS  BRACKETS. 


489 


centre  bolt,  which  holds  the  leaves  together,  and  the  outer  two 
of  which  are  for  clamp  bolts.  Five  bolts  are  used  by  some  de- 
signers. At  C  in  Fig.  335  is  shown  a  bracket  for  the  cross  mem- 
ber of  platform  springs  which  is  riveted  to  the  rear  cross  member 


FIG.  335.— REAR  SPRING  REAR  BRACKETS. 

of  the  frame.  In  order  to  prevent  twisting  of  this  frame  mem- 
ber it  is  well  to  run  diagonal  braces  from  the  side  rails  to  the 
middle  of  the  rear  cross  members,  as  shown.  French  designers 
usually  make  this  bracket  of  an  inverted  box  shape,  which  gives 
it  a  neater  form  but  interferes  with  riveting  at  the  centre  of 


490 


THE  FRAME  AND  ITS  BRACKETS. 


the  base.  Sometimes  this  bracket  is  of  considerably  greater 
length  than  here  illustrated,  while  one  designer  dispenses  with 
it  by  giving  the  frame  rear  cross  member  a  rearward  curve  at  the 
middle  and  clips  the  spring  to  it  directly. 

Spring  brackets  for  motor  trucks  differ  from  those  for  pleasure 
cars  on  account  of  the  difference  in  frame  construction  and  be- 
cause neat  appearance  is  not  such  an  important  factor.  Fig.  336, 
illustrates  two  designs  of  truck  spring  brackets.  That  shown  at 
A  is  a  front  bracket  and  is  riveted  to  the  front  corner  of  the 
frame.  However,  the  tendency  in  American  design  is  to  have 
the  frame  overhang  the  springs  in  front,  so  the  bracket  comes 


...L.i.  I           ^/    J 

K 
[' 

r  ,H  

L_j..j_  

0 

™  —  ^.s      \ 

22!    \ 

FIG.  336. — MOTOR  TRUCK  SPRING  BRACKETS. 

underneath  the  frame.  A  bracket  of  the  type  shown  at  B  is  used 
at  the  rear  end  of  the  front  springs  and  also  at  the  shackled  end 
or  ends  of  the  rear  springs. 

Radiator  Brackets. — Radiators  may  be  secured  either  to  the 
front  cross  member  or  to  the  side  rails.  Owing  to  their  rela- 
tively frail  construction  it  is  desirable  that  they  be  so  supported 
that  distortion  of  the  frame  will  not  strain  them  seriously.  The 
simplest  arrangement  consists  in  securing  brackets  to  the  sides 
of  the  radiator  which  are  bolted  down  to  the  top  flange  of  the 
side  rails  (A,  Fig.  337).  This,  of  course,  does  not  protect  the 
radiator  against  frame  distortion.  A  better  plan  consists  in  pro- 
viding the  radiator  with  trunnions  which  are  supported  in  bear- 
ings secured  to  the  frame  rail  (B,  Fig.  337).  The  top  then  is 


THE  FRAME  AND  ITS  BRACKETS. 


491 


braced  or  steadied  by  the  water  return  pipe  to  the  top  of  the 
engine  and  sometimes  by  a  rod  connecting  to  the  dashboard. 
Still  greater  protection  against  frame  distortion  can  be  secured 
by  slipping  bushings  with  spherical  seats  over  the  trunnions. 

In  the  case  of  commercial  vehicles  special  precautions  have  to  be 
taken  in  designing  the  support  for  the  radiator.  It  must  be  pro- 
tected from  both  road  vibration  and  strains  due  to  distortion  of 
the  frame.  The  radiator  is  insulated  against  road  vibration  by 
supporting  it  from  the  frame  through  the  intermediary  of  springs, 
coiled  compression  springs  being  generally  employed  and  flat 
springs  in  some  instances.  Strains  due  to  distortion  of  the  frame 
are  guarded  against  by  flexibly  supporting  the  radiator  at  three 
points.  It  is  carried  upon  springs  on  opposite  sides,  and  either 


FIG.  337.— RADIATOR  BRACKETS. 

the  top  or  the  bottom  is  braced  by  a  rod  to  some  part  of  the 
frame  or  body.  Sometimes  this  brace  is  also  spring  cushioned. 
Fig.  338  illustrates  the  Dayton  truck  radiator  support  which  pro- 
tects the  radiator  against  both  frame  distortion  and  road  vibra- 
tion, the  radiator  being  hung  on  coiled  springs  by  brackets  se- 
cured to  the  front  of  the  engine  housing. 

Fig.  339  illustrates  a  bracket  used  for  flexibly  supporting  the 
gear  box,  engine  or  unit  power  plant  at  three  points.  It  is  se- 
cured to  a  frame  member  by  three  bolts  and  is  provided  with  a 
forked  connection  which  joins  by  a  pivot  bolt  to  a  lug  on  the  part 
to  be  supported.  This  arrangement  affords  a  universal  support, 
which  protects  the  supported  part  against  any  distortion  of  the 
frame. 

Truck  Bumpers — Motor  truck  frames  generally  are  provided 
with  a  bumper  in  front  which  will  receive  the  shock  of  a  collision 


492  THE  FRAME  AND  ITS  BRACKETS. 


FIG.  338.— TRUCK  RADIATOR  SUPPORT. 


Top  View. 


Side    View. 


FIG.   339— UNIVERSAL  BRACKET  FOR  THREE  POINT   SUSPENSION. 


THE  FRAME  AND  ITS  BRACKETS. 


493 


and  transfer  it  directly  to  the  frame,  thus  protecting  frail  parts  at 
the  front  of  the  car,  such  as  lamps,  radiator,  etc.  These  bump- 
ers are  made  in  many  different  forms.  One  manufacturer  bends 
the  frame  side  rails  inward  in  a  curve  so  they  meet  at  the  middle 
of  the  car  where  they  are  joined  together  by  a  plate  riveted  to 
them.  Another  uses  a  sort  of  arch  formed  of  angle  iron  which 
is  riveted  to  the  side  frame  rails.  In  Fig.  340  is  shown  a  tubular 
bumper  carried  by  brackets  extending  forward  from  the  frame 


FIG.  340.— TRUCK  BUMPER. 


FIG.  341. — FENDER  BRACKETS. 

side  rails.  It  is  desirable  that  no  part  of  the  truck  project  ahead 
of  the  bumper,  and  for  this  reason  the  engine  starting  crank  is 
often  hinged  so  it  can  be  swung  out  of  the  way. 

The  brackets  supporting  the  front  fenders  should  preferably 
be  secured  to  the  frame  in  such  a  manner  that  the  fenders  can 
be  quickly  removed,  for  the  reason  that  the  latter  generally  inter- 
fere considerably  with  any  important  work  on  the  engine.  A 
method  of  securing  the  brackets  which  insures  this  quick  re- 
moval is  illustrated  in  Fig.  341.  A  small  bracket  is  reamed  with 
a  taper  hole  to  receive  the  fender  hanger.  It  is  apparent  that 


494 


THE  FRAME  AND  ITS  BRACKETS. 


with  a  bracket  of  this  kind  the  fender  can  be  quickly  taken  off. 
The  same  type  of  bracket  may  be  used  for  the  searchlight,  and, 
in  an  inverted  position  for  the  running  board  hangers.  Rear 
fender  brackets  are  generally  riveted  to  the  frame,  but  can  be 
made  detachable  at  very  little  extra  expense.  The  design  for 
such  a  detachable  bracket  is  also  shown  in  Fig.  341.  Fender 
irons  often  are  bolted  to  lugs  formed  on  radiator  or  spring 
brackets. 

Fig.  315  illustrates  a  design  of  step  or  running  board  hanger 
of  which  it  is  customary  to  use  three  on  each  side  in  pleasure 
cars  and  two  in  trucks.  This  hanger  is  made  of  pressed  steel 
and  has  a  channel  section  which  varies  with  the  load.  The  one 


X)  O  O' 
A 


n 


FIG.  342. — STEP  HANGER. 


here  shown  is  secured  to  the  frame  by  three  rivets  all  in  a  line. 
Another  plan  consists  in  making  the  base  flaps  of  substantially 
rectangular  section  and  using  four  rivets. 

Starting  Crank  Bracket—In  many  cars  the  bracket  for  the 
engine  starting  crank  is  secured  to  the  frame  front  cross  mem- 
ber, as  illustrated  in  Fig.  343.  Instead  of  the  hub  of  the  bracket 
being  on  the  under  side  of  the  cross  member  it  may  be  so  located 
that  the  shank  of  the  starting  crank  has  to  pass  through  a  hole 


THE  FRAME  AND  ITS  BRACKETS. 


495 


FIG.   343. — STARTING   CRANK   BRACKET. 

in  the  cross  member,  the  bracket  being  riveted  to  the  web  of  the 
channel  either  in  front  or  in  the  back.  The  crank  and  bracket 
show  provisions  made  for  automatically  holding  the  former  in 
the  upright  position  when  disengaged. 

Lamp  Brackets — Of  the  different  lamps  carried  on  an  auto- 
mobile the  head  and  tail  lights  are  usually  supported  by  brackets 
secured  to  the  frame.  Fig.  344  shows  two  designs  of  head  light 
brackets  and  one  tail  light  bracket  At  A  is  shown  a  drop 
forged  bracket  which  fits  with  a  taper  joint  into  a  bracket  riveted 


FIG.  344. — LAMP  BRACKETS. 


496  THE  FRAME  AND  ITS  BRACKETS. 

to  the  frame  side  rail.  One  designer  places  the  frame  bracket 
inside  the  channel,  passing  the  shank  of  the  lamp  bracket  through 
a  hole  in  the  top  flange,  which  makes  for  neat  appearance.  In 
the  headlight  bracket  design  shown  at  B  the  prongs  are  bolted  to 
the  shank,  which  makes  the  distance  between  prongs  adjustable. 
Headlamp  brackets  have  been  standardized  by  the  Society  of 
Automobile  Engineers.  Three  standard  sizes  are  recommended 
for  the  forked  type  of  head-lamp  support,  the  forks  having  cen- 
tre-to-centre widths  of  7]/4,  &/4  and  9%  in.  The  upper  ends  of 
the  supports  are  to  be  Y2  in.  diameter,  with  y2  in.  S.  A.  E.  threads 
and  machined  shoulders  not  less  than  ^  in.  diameter.  The  dis- 
tance from  the  upper  face  of  the  shoulder  to  the  last  full  thread 
on  the  end  of  the  support  should  not  be  less  than  \l/2  in.  where 
no  tie-rod  is  used,  or  ll/2  in.  plus  thickness  of  rod  where  a  rod 
is  used.  The  use  of  nuts  and  lock  washers  for  locking  the  lamp 
to  the  fork  is  standard  practice. 

An  adjustment  should  be  provided  for  the  support  to  allow 

a  change  of  the  vertical  angle  of  the  lamp  without  bending  any 

part  of  the  support    The  lugs  attached  to  the  lamp  shells  should 

have  bores  of  17/32  in.,  the  bores  being  \l/2  in.  long.    The  center- 

f  the  hole  in  the  lug  should  be  not  less  than  9/16  in.  from 

arest  point  of  the  shell.    The  clearance  between  the  lower 

f  the  bracket  and  the  lamp  should  not  be  less  than  9/16  in. 


CHAPTER  XVIII. 


SPRINGS. 

Automobile  frames  are  supported  on  the  axles  through  the  in- 
termediary of  steel  springs.  Leaf  springs,  built  up  of  a  number 
of  leaves  or  plates  of  different  lengths,  are  used  almost  exclusive- 
ly, though  coiled  springs  have  been  used  on  low  priced  cars. 

Classification  of  Springs — The  simplest  form  of  automobile 
spring  is  the  half  elliptic  spring  illustrated  in  Fig.  345  at  A.  It 
is  made  up  of  one  master  leaf  whose  ends  are  formed  into  an  eye 
for  connection  to  the  spring  brackets  or  shackles,  and  a  number 
of  shorter  leaves,  the  lengths  of  the  leaves  decreasing  uniformly 
with  their  distance  from  the  master  leaf,  except  that  in  springs 
for  heavy  loads  the  leaf  or  leaves  nearest  the  master  leaf  some- 
times extend  to  the  ends  of  the  latter  and  even  enwrap  the 
spring  eyes.  '  The  various  leaves  of  a  spring  are  held  together 
by  a  centre  bolt. 

All  other  types  of  springs  are  made  up  wholly  or  in  part  of 
half  elliptic  springs.  At  B,  Fig.  345,  is  shown  the  three-quarter 
elliptic  spring,  which  consists  of  a  quarter  elliptic  top  member  and 
a  half  elliptic  bottom  member,  the  two  members  being  joined  by  a 
bolt  at  one  end.  At  C  is  shown  the  elliptic  spring,  consisting  of 
half  elliptic  top  and  bottom  members  which  are  joined  by  bolts  at 
both  ends.  D  shows  the  three-quarter  scroll  elliptic,  consisting  of 
a  quarter  elliptic  scroll  top  member  and  a  half  elliptic  bottom 
member,  joined  by  shackles  at  one  end.  E  shows  the  scroll  el- 
liptic (one  end)  spring,  consisting  of  a  half  elliptic  top  member 
with  a  scroll  at  one  end  and  a  half  elliptic  bottom  member,  joined 
at  one  end  by  a  bolt  and  at  the  other  by  shackles.  The  spring 
shown  at  F  is  known  as  the  scroll  elliptic  (both  ends)  ;  it  con- 
sists of  a  half  elliptic  top  member  with  scrolls  at  both  ends  and  a 
half  elliptic  bottom  member,  the  two  being  joined  by  shackles  at 
both  ends.  At  G,  Fig.  346,  is  shown  a  platform  spring  (three 
point  suspension),  which  consists  of  two  half  elliptic  side  mem- 
bers and  one  half  elliptic  cross  member,  the  side  members  being 

497 


498 


SPRINGS. 


FIG.  345— BODY  SPRING  TYPES. 


SPRINGS.  409 

joined  to  the  cross  member  by  shackles.  At  H  is  shown  a  three- 
quarter  elliptic  platform  spring  consisting  of  two  three-quarter 
elliptic  side  members  and  one  half-elliptic  cross  member,  the  side 
members  being  joined  to  the  cross  members  by  shackles.  /  shows 
an  auxiliary  spring  consisting  of  a  half  elliptic  spring  with  plain 
ends. 


346.— BODY  SPRING  TYPES. 


In  Fig.  347  is  shown  a  half  elliptic  cantilever  or  floating  canti- 
lever type  of  spring.  This  is  mainly  used  for  rear  suspension  of 
pleasure  cars.  It  is  a 'half  elliptic  spring  which  swivels  on  the  car 
frame  at  its  middle,  is  shackled  to  the  frame  at  the  forward  end 
and  connects  to  the  axle  at  its  rear  end.  Quarter  elliptic  springs, 
which  are  also  classed  as  cantilever  springs,  are  used  for  both 
front  and  rear  suspension  on  light  cars.  The  heavy  end  of  these 
is  secured  to  the  frame  and  the  light  end  to  the  axle. 


500 


SPRINGS. 


FIG.  347. — GRANT  CANTILEVER  SPRING. 


Spring  Material. — The  common  spring  material  which  has 
long  been  used  for  carriage  and  railway  springs  is  a  carbon  steel 
containing  about  I  per  cent,  of  carbon.  The  S.  A.  E.  specifica- 
tions for  this  carbon  spring  steel  are  as  follows : 

0.95   CARBON  STEEL. 

Carbon     0.90101.05%   (0.95%  desired) 

Manganese 0.25100.50%    (0.35%  desired) 

Silicon      o.  10  to  0.30% 

Phosphorus,    not    over 0.035% 

Sulphur,    not    over 0.035% 

The  natural  sources  of  the  above  steel  are  the  basic  open 
hearth,  crucible  and  electric  furnace.  This  grade  of  spring  steel 
is  suited  for  the  most  important  springs,  as  with  proper  heat 
treatment  it  will  give  very  good  results.  The  heat  treatment  of 
the  spring  plates  after  they  are  worked  to  shape  consists  in 
quenching  in  oil  at  a  temperature  of  about  1,400  degrees  Fahr., 
reheating  to  about  500  degrees  Fahr.  and  cooling  slowly.  The 
temperatures  are  given  for  purposes  of  illustration  only.  The 
physical  qualities  of  the  completed  spring  will  greatly  depend 
upon  them,  and  the  best  quenching  and  reheating  temperatures 
are  usually  worked  out  by  experiment  in  each  shop. 

The  carbon  steel  above  specified  when  tempered  will  have  the 
following  physical  properties,  according  to  the  heat  treatment: 

Tensile     strength 120,000  to  180,000  Ibs.  per  sq.  in. 

Elastic     limit 70,000  to    95,000  Ibs.  per  sq.  in. 

Elongation    in    2    inches 9  to  10% 

Reduction    of   area 14  to  16% 

Besides  carbon  steel,  chrome-nickel  steel,  chrome-vanadium 
steel  and  silico  manganese  steel  are  used  in  the  manufacture  of 
springs.  The  S.  A.  E.  specifications  of  silico  manganese  spring 
steel  are  as  follows: 


SPRINGS.  501 

SILICO-MANGANESE   STEEL. 

Carbon     0.45  to  0.55%  (0.50%  desired) 

Manganese     o .  60  to  o . 80%  (o .  70%  desired) 

Silicon     i .  90  to  2 . 20%  (2%  desired) 

Phosphorus,   not   over 0.04% 

Sulphur,   not  over 0.04% 

The  following  heat  treatment  will  probably  give  good  results: 
Heat  to  1,600-1,750  degrees  Fahr.,  quench,  reheat  to  about  800 
degrees  Fahr.  and  cool  slowly.  The  best  reheating  temperature 
should  be  carefully  determined  by  experiment.  The  elastic  limit 
will  be  about  150,000  pounds  per  square  inch. 

Krupp's  silico  manganese  spring  steel  is  claimed  to  have  the 
following  physical  properties  when  spring  tempered : 

Tensile     strength 250,000  to  255,000  ibs.  per  sq.  iw 

Elastic     limit 206,000  Ibs.  per  sq.  in. 

Elongation    3-5% 

Chrome  nickel  and  chrome  vanadium  steels  vary  in  composi- 
tion and  different  heat  treatments  result  in  different  physical 

-1 


/'~                                                                  s                                                              \ 

>                         .y 

^- 

w 

FIG.  348. 

qualities,  but  either  steel  properly  spring  tempered  should  have 
an  elastic  limit  upward  of  150,000  pounds  per  square  inch. 

Theory  of  Leaf  Springs—  The  simplest  form  of  leaf  spring 
is  that  containing  only  a  single  leaf.  Such  a  spring  may  be  con- 
sidered either  as  two  cantilever  beams  loaded  at  their  ends  or  as 
a  simple  beam  loaded  at  the  middle.  Fig.  348  represents  such  a 
spring  in  diagram.  If  we  consider  each  half  of  the  spring  as  a 
cantilever  and  denote  the  load  on  one  end  of  the  spring  by  P,  the 
half  length  of  the  spring  by  /,  the  width  by  b,  the  thickness  by  t 
and  the  coefficient  of  elasticity  by  E,  we  have  for  the  deflection  of 
the  end  of  the  spring 

d=    i     PI*       4/V3 
3     El   ~  Ebi*> 

(See  cantilever  beams  in  any  textbook  on  mechanics.)  The 
bending  moment  at  any  distance  x  from  the  end  of  the  spring  is 
P  x  and  the  stress  in  the  material  at  that  point  is 


bcf 


502  SPRINGS. 

Hence,  with  a  single  leaf  of  uniform  section  over  its  whole 
length  the  stress  due  to  the  bending  moment  varies  from  nothing 
at  the  end  to  a  maximum  at  the  middle  of  the  spring.  There- 
fore, if  a  single  uniform  section  leaf  were  used  the  material 
would  be  very  poorly  utilized,  and  one  of  the  objects  in  using 
a  multiple  leaf  spring  is  to  make  the  stress  substantially  uniform 
in  all  parts  of  the  spring.  Now  suppose  we  took  a  number  of 
equal  leaves  and  assembled  them  as  shown  in  Fig.  349.  Then, 
if  loads  were  applied  to  the  top  leaf,  all  of  the  leaves  would  be 
deflected  the  same  amount.  If  there  are  n  leaves  the  deflection 
would  be  the  same  as  in  the  case  of  a  single  leaf  subjected  to  a 

t> 

load . .  Therefore  the  deflection  of  a  spring  like  that  shown  in 

n 
Fig.  321  should  be 

4-Pf 


Enbt3 
-1 *- 


Iw 

FIG.  349. 

However,  in  a  multiple  leaf  spring  there  can  be  no  deflection 
without  one  leaf  sliding  over  another,  which  introduces  the  factor 
of  friction.  As  a  leaf  of  the  spring  deflects  there  are  two  forces 
at  work,  viz.,  the  force  due  to  the  load  P  carried,  and  the  force 
due  to  the  internal  strains.  The  former  force  is  constant,  but  the 
latter  increase  from  nothing  at  the  moment  the  deflection  begins 
to  the  value  of  the  former  when  it  attains  its  maximum  (in  a 
single  leaf  spring).  In  a  multiple  leaf  spring  the  friction  between 
leaves  is  opposed  to  the  deflection  and,  therefore,  assists  the  in- 
ternal forces  or  those  due  to  the  strains  in  the  material.  While 
the  spring  is  deflecting  the  difference  between  the  force  due  to 
the  load  on  the  spring  and  that  due  to  the  internal  strain  is 
available  for  overcoming  the  frictional  resistance,  and  it  is  ob- 
vious that  when  this  difference  becomes  equal  to  the  frictional 
force  the  deflection  ceases.  Hence  the  deflection  will  be  re- 
duced and  an  allowance  must  be  made  for  leaf  friction.  This 
reduction  varies  with  the  number  of  leaves,  but  the  allowance 
may  be  placed  at  15  per  cent,  for  practical  cases. 


SPRINGS.  503 

In  an  actual  vehicle  spring  the  leaves  are  of  gradually  decreas- 
ing lengths,  and  since  the  outer  end  of  any  leaf  is  not  supported 
by  leaves  below  it,  the  deflection  will  be  greater  than  in  a  spring 
of  the  form  shown  in  Fig.  349.  Reuleaux  has  calculated  that  if 
the  lengths  of  springs  decrease  uniformly,  as  in  Fig.  350,  the 
multiplying  factor  will  be  1.5.  That  is,  a  spring  of  the  type 
shown  in  Fig.  350  will  deflect  50  per  cent,  more  for  a  given  load 
than  a  spring  of  the  type  shown  in  Fig.  349,  both  being  of  the 
same  dimensions.  However,  in  automobile  springs  the  second 
leaf  often  extends  out  as  far  as  the  centre  of  the  spring  eye,  and 
in  heavy  motor  truck  springs  even  two  or  three  leaves  support 
the  main  leaf  at  the  eyes,  in  which  case  the  multiplying  factor  is 
smaller.  From  the  value  of  this  factor  for  the  extreme  cases, 
Figs.  349  and  350,  viz.,  1  and  1.5,  its  value  for  any  intermediate 
case  can  be  closely  approximated.  For  commercial  springs  it 
probably  never  drops  below  1.25.  Hence,  taking  1.25  and  1.5  as 


FIG.  350. 

the  extreme  values  of  this  factor  in  actual  practice,  and  taking 
into  account  the  effects  of  both  shortening  of  the  leaves  and  of 
friction  between  them,  we  have  for  the  deflection  of  vehicle  leaf 
springs 

(1.25  to  1.5)   (1  —  0.15)  4PP 
d=  - 

Enbt3 
which  may  be  simplified  to  read 


_  (76) 

E  n  b  r 
The  larger  coefficient  is  to  be  used  when  the  length  of  any  leaf  is 

less  than  that  of  the  preceding  one  by  —  ;  the  smaller  if  several 

n 

of  the  longer  leaves  are  substantially  equal  in  effective  length. 

Equation  (76)  covers  the  case  of  a  spring  with  leaves  of  equal 
thickness.    If  the  thickness  t  differs  we  may  substitute  for  n  t*  in 
the  denominator,  ^3  +  1?  +  t£  .................  ....    .  /n3,  or  2  t'A, 

which  gives 


504  SPRINGS. 

The  bending  moment  at  the  middle  of  the  spring  is  equal  to 
PI.    In  a  spring  having  n  leaves  of  equal  thickness  t,  this  bending 

p   J 

moment  is  equally  divided  and  that  on  each  leaf  is  —  .     Since 

n 

the  section  modulus  of  the  leaf  is  ,  the  unit  stress  is 

6 
PI 

n  6  PI 


bt*  "~  nbt2 

6 

If  we  divide  the  elastic  limit  of  the  material  by  this  stress  we  ob- 
tain the  factor  of  safety,  which  in  well  designed  springs  is  usually 
between  2.5  and  2.75.  Therefore,  calling  the  elastic  limit  of  the 
spring  material  L,  the  maximum  safe  load  on  the  spring  with 
a  safety  factor  of  2.5, 

W=Lnbt\ (78) 

In  case  the  leaves  are  of  unequal  thickness  we  can  calculate  the 
strain  in  each  from  the  fact  that  the  elastic  curves  of  all  leaves 
at  the  middle  must  be  alike.  Under  these  conditions  the  moment 
coming  on  each  leaf  is  proportional  to  its  moment  of  inertia. 
The  bending  moment  on  the  heaviest  leaf  (of  moment  of  inertia 
/)  then  will  be 


. 

and  the  unit  stress  in  this  leaf  will  be 
Pit? 

s-™=*r,± (79) 

bt?        b  Z  tA 

In  the  design  of  the  springs  the  designer  has  to  deal  with  a 
considerable  number  of  variable  factors,  viz.,  the  length,  width, 
thickness  and  number  of  leaves,  and  the  elastic  limit  of  the  ma- 
terial. Of  these  the  first  two  are  generally  determined  by  em- 
pirical rules  based  upon  experience.  Longer  springs  make  for 
an  easier  riding  car,  because  with  a  greater  length  a  greater  de- 
flection can  be  obtained  for  a  given  change  in  load  without  in- 
creasing the  stress  in  the  material.  Thus,  the  stress  will  remain 
the  same  if 

t~t2 
and  under  these  conditions 


SPRINGS. 


505 


The  usual  lengths  of  different  kinds  of  front  and  rear  springs  in 

pleasure  cars   are   given    in    the   following   table   taken    from   a 

book  on  Leaf  Springs,  compiled  by  David  Landau,  and  published 

by  the  Sheldon  Spring  and  Axle  Co.     The  loads  referred  to  in 

the  table  are  those  which  the  springs  will  carry  when  the  car 

is  loaded  with  its  rated  number  of  passengers,  and  the  lengths 

are  those  which  the  springs  will  have  when  so  loaded. 

TABLE   XI— PLEASURE   CAR    SPRINGS. 

FRONT  SPRING,  SEMI-ELLIPTIC. 


Load  on  One  Spring, 

Length, 

Width. 

Pounds. 

Inches. 

Inches. 

350  to     400     .... 

33      to  34 

1/2 

400  to     500    

35      to  36 

i* 

500  to     550    

36      to  37J4 

i* 

600  to     800   

37l/a  to  40 

2 

800  to  1,100    

40      to  42 

2*A 

REAR  HALF  ELLIPTIC  SPRINGS. 

Load  on  One  Spring, 

Length, 

Width, 

Pounds. 

Inches. 

Inches. 

450  to     550    

46      to  48 

I* 

55U  to     650    

49      to  50 

2 

700  to     850    

51       to  52 

2 

900  to  1,000    

52      to  55 

2J4 

i.ooo  to  1,350   

55       to   57 

2*A 

1,350  to  1,550    

57       to  60 

2J4  t02j4 

RE, 

IR  SPRINGS,  THREE-QUARTER  ELLIPTIC. 

Semi-Elliptic         Length  of  Scroll 

Load  on  One  Spring, 

Element,           (Link  to  Bolt), 

Width, 

Pounds. 

Inches.                     Inches. 

Inches. 

450  to     500  

45      to  47                18      to  19 

iH 

500  to     650    

47      to  49                18      to  19 

rtf 

650  to     775    

47T/2to  51*6            ig  Y2  to  22 

775  to     900    

S*J/2  to  52               22J4  to  23 

to  2J4 

S2*/2  to  53^            23      to  24 

to  2J4 

1,000  to    ,150   

$3l/2  to  54                24      to  25 

tO    2J4 

1,150  to    ,250   

54      to  54^            25      to  25^ 

to  2*A 

1,250  to    ,350  

5454  to  55                25^  to  26 

to  2M 

i,35^  to    ,450    

55      to  56                26      to  26j£ 

'A  to  zya 

1,450  to    ,550   

56      to  58                26^2  to  27 

2^4  to  zy* 

1,550  to    ,650    

58      to  60                27      to  27}^ 

2V*  tO    2J4 

FULL  ELLIPTIC  SPRINGS. 

Load  on  One  Spring, 

Length, 

Width, 

Pounds. 

Inches. 

Inches. 

500  to     700    

35 

I* 

800    

36 

2 

1,000      

37 

2J4 

1,100     

39 

2% 

,200    

41 

2Y4 

300     

43 

2% 

,400    

44 

2K 

,500     

45 

2V* 

.600    

46 

*K 

506 


SPRINGS. 


THREE-QUARTER   PLATFORM   SPRINGS. 


Load  on 

One  Side  Spring, 
Pounds. 

500  to     550  . 

600  to     700  . 

900  . 

,000  . 


,100 
,200 
,300 
,400 
,500 


Length  of 

Side  Spring, 
Inches. 

45  to  47 
,  47  to  49 
,  51  to  53 
,  53  to  55 
.  55  to  57 

57 

57^ 

58 

58^ 


Length  of 
Cross  Spring, 

Inches. 
39^ 
39^ 

39^  to  40 
39l/2  to  40 
39J4  to  40 
40 
40 
40 
40 


Width, 
Inches. 

1M 

2     to  2yA 


2Y4 

2Y4 
2Y* 
2Y* 


The  author  has  compiled  the  following  figures  on  the  average 
lengths  and  widths  of  springs  used  on  motor  trucks : 

TABLE  XII— MOTOR  TRUCK   SPRINGS. 
FRONT    SPRINGS,    HALF    ELLIPTIC. 

Load  Capacity,  Length,  Width, 

Tons.  Inches.  Inches. 

3/4    ' 38  to  40  2 

1        38  to  40  2J4 

11/2    40  to  42  2*/2 

2        42  to  44  2V* 

3        44  to  46  2Y2  to  3 

4 46  to  48  3 

5        48  to  50  3 

REAR   SPRINGS,   HALF   ELLIPTIC. 

Load  Capacity,  Length,  Width, 

Tons.  Inches.  Inches. 

3/4    48  to  52  2 

1         48  to  52  2Y4 

\y2  so  to  53  2y2 

2 50  to  53  2l/2 

3        52  to  54  3 

4        52  to  55  3 

5        54  to  56  $y2 

PLATFORM   SPRINGS,   SIDE   MEMBERS. 

Load  Capacity,  Length,  Width, 

Tons.  Inches.  Inches. 

3^ 44  to  48  2 

1        44  to  48  2*A 

1 J4    46  to  48  2  J4 

2        46  to  49  2Yz 

3        48  to  50  3 

4        48  to  51  3 

5        50  to  3^ 

Width  and  Thickness  of  Leaves. — It  has  long  been  custom- 
ary to  make  spring  plates  according  to  the  Birmingham  or  Stubb's 


SPRINGS.  507 

gauge,  and  the  following  table  gives  the  sizes  employed,  together 
with  the  cubes  of  the  thickness,  for  convenience  in  calculating  de- 
flections and  maximum  safe  loads  : 

No.  Thickness  (Inch).  t3 

oo     0.380  0.05^9 

0     0.340  0.0393 

1     0.300  0.0270 

2       0.284  O.O229 

3  0.259  0.0174 

4  0.238  0.0135 

5 0.220  0.0106 

6  0.203  0.0084 

Owing  to  the  non-uniform  variations  in  thickness  in  the  Stubb's 
gauge  some  manufacturers  are  having  plates  rolled  varying  in 
thirty-seconds  of  an  inch. 

Thickness  (Inch).  t5 

0-375  0.0527 

0.344  0.0407 

0.312  0.0304 

0.28l   O.O222 

0.25O   0.0156 

O.2I9   O.OIO5 

0.187   • 0.0065 

Spring  plates  are  made  in  the  following  standard  widths :  For 
pleasure  cars:  il/2,  1^4,  2,  2%  and  2,l/2  inches.  For  commercial: 
2,  2J4,  2l/2t  3,  3^,  4  and  4^  inches. 

Flexibility — The  flexibility  is  a  most  important  quality,  as  an 
insufficiently  flexible  spring  makes  the  car  hard  riding,  while  a 
spring  too  flexible  will  cause  the  chassis  frame  to  strike  the  axles 
and  is  liable  to  break.  Spring  makers  rate  or  gauge  springs  by 
the  load  required  to  deflect  them  one  inch.  From  the  automobile 
designer's  standpoint  the  most  important  factor  is  the  deflection 
caused  by  the  maximum  dead  load  the  springs  will  have  to  bear. 
This  total  deflection  should  increase  with  the  length  of  the  spring, 
because,  on  the  one  hand,  long  springs  are  used  on  high  pow- 
ered, luxurious  vehicles  which  are  naturally  expected  to  be  easier 
riding  than  small  cars,  and,  on  the  other  hand,  a  greater  deflec- 
tion can  be  obtained  with  the  larger  springs  without  increasing 
the  stress  in  the  material.  Since  the  length,  width,  etc.,  of  the 
springs  are  empirically  chosen,  it  is  obvious  that  thare  can  be  no 
rational  relation  between  the  length  of  the  springs  and  their  de^ 
flection  under  their  maximum  dead  load,  but  data  on  hand  shows 
that  in  practice  the  two  factors  mentioned  vary  substantially  in 
direct  proportion. 


508  SPRINGS. 

The  deflection  should  also  increase  somewhat  with  the  elastic 
limit  of  the  material.  Of  course,  if  we  make  two  springs  of  ex- 
actly the  same  dimensions,  the  one  of  ordinary  carbon  spring 
steel  and  the  other  of  alloy  spring  steel,  they  will  deflect  equally 
under  equal  loads,  because  both  steels  have  substantially  the  same 
coefficient  of  elasticity.  But  that  is  not  the  proper  way  to  use 
alloy  steel.  Wherever  alloy  steel  is  substituted  for  carbon  steel — 
except  in  cases  where  the  original  design  proved  far  too  weak — 
the  weight  of  the  part  is  reduced.  Therefore,  with  alloy  steel  in 
place  of  carbon  steel  we  would  use  thinner  leaves,  which  would 
deflect  more.  The  higher  elastic  limit  of  the  alloy  steel  enables 
it  to  withstand  this  higher  deflection.  Viewing  the  subject  from 
another  standpoint,  if  it  were  not  possible  to  secure  better  riding 
qualities  there  would  be  little  object  in  using  alloy  steels  for 
springs.  A  spring  can  be  made  adequately  strong  of  carbon  steel, 
but  designed  mainly  with  a  view  to  strength,  such  a  spring  is  apt 
to  be  rather  hard  riding. 

As  spring  steel  is  a  rather  expensive  material  the  weight  of 
steel  required  for  the  springs  is  an  important  item.  It  will  be 
shown  further  on  that  for  a  given  deflection  and  a  given  stress 
in  the  steel  the  same  weight  of  steel  is  required  whatever  the  type 
of  spring  used.  However,  the  more  complicated  types,  like  three- 
quarter  and  full  elliptic,  are  more  likely  to  be  used  when  large 
deflections  are  wanted,  and  vice  versa,  the  simplest  type,  the 
quarter  elliptic,  is  most  likely  to  be  selected  when  it  is  desired 
to  keep  down  the  cost  of  the  springs. 

The  following  table  shows  the  deflection  ranges  with  the  dif- 
ferent types  of  springs. 

TABLE  XIII.   RANGE  OF  DEFLECTION  UNDER  DEAD 

LOAD 

Half  Elliptic  front     1^4—2  inches 

Half  Elliptic  rear     3V2—  5V2  inches 

Three   Quarter   Elliptic   rear 4    — 6%  inches 

414 — gi/,  incluv; 

Truck  Half  Elliptic  front     2*4—  3%  inches 

Truck  Half  Elliptic  rear    2%— 3%  inches 

Truck  platform     3&— 4%  inches 

It  will  be  seen  that  the  half  elliptic  front  springs  of  pleasure 
cars  deflect  less  than  half  as  much  as  rear  springs  of  the  same 
type.  One  reason  for  thus  limiting  the  play  of  the  front  springs 
is  the  desire  to  minimize  its  effect  on  steering.  Another  is  that 
it  permits  of  lowering  the  frame,  since  not  so  much  clearance  be- 
tween frame  and  axle  is  required.  As  regards  the  various  types 
of  rear  springs,  it  is  obvious  that  the  greater  the  relative  length  of 
the  spring  the  greater  the  deflection  under  full  load  can  be  made; 
that  is,  a  three  quarter  elliptic  or  platform  spring  will  deflect 
more  than  a  half  elliptic,  and  an  elliptic  spring  most  of  all. 


SPRINGS.  509 

As  far  as  pleasure  car  rear  springs  are  concerned,  the  initial 
deflection  under  load  to  be  allowed  for  is  chiefly  a  commercial 
question.  The  greater  the  initial  deflection — load  and  quality  of 
spring  steel  being  the  same — the  greater  the  weight  of  the  springs 
required,  and  the  higher  their  cost.  The  greater  deflections  given 
in  the  tabulation  are  therefore  found  on  the  higher  priced  cars. 
Eccentrated  Springs — The  formulae  for  deflection  and  maxi- 
mum safe  load  developed  in  the  foregoing  apply  directly  only  to 
half  elliptic  springs.  It  is  obvious  that  the  deflection  of  an  elliptic 
spring  under  a  given  load  is  twice  that  of  one  of  its  half  elliptic 
members  under  the  same  load.  In  three  -quarter  elliptic  and  plat- 
form springs  the  case  is  slightly  more  complicated.  If  the  axle 
were  secured  to  the  middle  of  the  length  of  the  half  elliptic  or 
side  member,  the  ends  of  the  spring  would  deflect  unequally, 
which  would  cause  the  axle  housing  to  constantly  rock  around  its 
axis  under  the  play  of  the  springs,  or  the  spring  saddle  to  rock 


FIG.  351. — ECCENTRATED  THREE-QUARTER  ELLIPTIC  SPRING. 

on  the  axle  housing,  both  of  which  are  objectionable.  In  the 
above  case  there  are  two  quarter  elliptic  springs  in  series  on  one 
side  of  the  axle,  while  there  is  only  a  single  quarter  elliptic  on 
the  other  side,  and  the  combined  deflection  of  the  two  quarter 
elliptics  would  be  twice  that  of  the  single  elliptic.  In  order  to 
overcome  this  defect,  the  half  elliptic  or  side  spring  is  usually 
"eccentrated ;"  that  is,  the  centre  of  its  support  on  the  axle  is  at 
unequal  distances  from  the  spring  eyes.  That  end  of  the  half 
elliptic  or  side  member  which  is  shackled  to  the  frame  must  be 
so  much  longer  than  the  other  end  that  under  a  given  load  it  will 
deflect  as  much  as  the  other  two  quarter  elliptics  together.  The 
proper  amount  of  eccentration  can  easily  be  calculated  for  a  three 
quarter  elliptic,  provided  the  two  rear  quarter  elliptics  are  of  equal 
length.  Since  the  width,  thickness  and  number  of  leaves  of  each 
of  the  three-quarter  elliptics  in  Fig.  351  are  the  same  we  have  by 
equation  (76). 


510  SPRINGS. 


11=^2J2^  1.264 

For  practical  purposes  a  coefficient  of  1.25  would  be  sufficiently 
close,  which  makes  the  two  lengths  as  4  to  5.  If  the  springs  are 
thus  arranged  the  deflection  can  be  calculated  by  assuming  that  the 
longer  end  of  the  half  elliptic  member  carries  one-half  the  total 
load  and  calculating  its  deflection  under  this  load,  which  will  be 
equal  to  the  deflection  of  the  whole  spring.  In  a  platform  spring  the 
length  of  the  cross  member  is  independent  of  that  of  the  side 
member.  In  order  to  find  the  proper  eccentration  for  the  side 
member  of  a  platform  spring  proceed  as  follows  :  Assume  one- 
quarter  of  the  total  load  on  the  rear  springs  to  be  supported 
by  one-half  of  the  cross  member,  and  by  means  of  equation  (76) 
calculate  its  deflection.  Denote  this  by  ds.  Now,  denoting  the 
deflection  of  the  long  end  of  the  side  member  by  d\  and  that  of 
the  short  end  by  d*f  we  have 

di  =  d*  +  d* 
According  to  equation  (76). 

5.1  P  /x3       5.1  P  h5 


E  n  b  t*       E  n  b  t* 
E  n  b  f 
h3  —  I?  = 


5.1  P 
We  also  have  /t  _j_  /8  =  L 

These  two  simultaneous  equations  can  readily  be  solved  after 
the  arithmetic  values  are  inserted  in  the  right  hand  terms. 

Front  half  elliptic  springs  also  are  sometimes  eccentrated,  the 
object  being  to  increase  the  wheelbase  without  increasing  the 
length  of  the  car. 

Number    and    Thickness    of    Plates—The    deflection   of  a 
cantilever  loaded  at  the  end  is  given  by  the  equation 
,        W* 


and  the  maximum  stress  in  the  material  of  such  a  lever  is 

Wlc       Wit 

s=s-r~rr 

Hence 

— 

and 


SPRINGS.  511 

Placing  the  coefficient  of  elasticity  E  at  28,000,000  this  reduces  to 


42,000,000  d 

The  gauge  thickness  closest  to  the  result  obtained  should  then 
be  chosen,  and  if  the  result  should  come  midway  between  the 
thicknesses  of  two  gauge  sizes,  the  length  of  the  spring  could 
be  varied  slightly  and  the  calculation  made  over.     After  t  has 
been  determined  the  necessary  number  of  leaves  may  be  deter- 
mined by  a  transformation  of  equation  (76)  as  follows : 
« 
— (82) 


Sample  Calculation — To  illustrate  the  use  of  the  formu-lae 
derived  in  the  foregoing,  we  will  calculate  the  springs  for  a  five 
passenger  touring  car  in  which  each  of  the  half  elliptic  front 
springs  has  to  carry  650  pounds  and  each  of  the  three  quarter 
elliptic  rear  springs  850  pounds.  From  Table  XI  we  find  the 
proper  size  of  front  springs  to  be  38x2  inches  and  the  proper 
size  of  the  rear  springs,  52  x  2  +  23  x  2  inches. 

We  will  assume  that  carbon  spring  steel,  with  an  elastic 
limit  of  about  135,000  pounds  per  square  inch,  is  to  be  used 
for  the  front  springs,  so  that  a  stress  of  50,000  pounds  per 
square  inch  can  be  figured  on.  The  deflection  of  the  springs 
under  full  load  would  be  about  1%  inches.  Then,  inserting 
values  in  equation  (81)  we  find  for  the  necessary  thickness  of 
plates. 

50,000  X   102 

t  = =  0.286  say  0.284  inch 

42,000,000  X  1.5 

Inserting  values  in  equation    (82)   we  get  for  the  number  of 
leaves  required 

5.1   X   325  X   193 

n  =  =  5.92 

28,000,000   X    1.5   X   2   X   0.284s 

Therefore,  six  leaves  would  be  chosen.     The  actual  deflection 
then  would  be  equation  (76) 

5.1  X   325  X   198 

d  =  «=  1.48  inches 

28,000,000   X   6   X   2   X   0.284s 

and  the  actual  stress 

42,000,000   X   1.48   X   0.284 

8  =  =  48,900  Ibs.  p.  sq.  in. 

192 

The  rear  springs,  we  will  assume,  are  to  be  made  of  alloy 
spring  steel,  which   will   sustain   a   stress   of   75.-000   Ibs.    per 


512 


SPRINGS. 


square  inch.  The  deflection  of  the  rear  springs  under  load  may 
be  chosen  at  5  inches.  The  long  end  of  the  half  elliptic  mem- 
ber will  be  52  —  23  =  29  inches  long.  Inserting  values  in 
equation  (81) 

75,000  X  292 

t  = =  0.300 

42,000,000  X  5 

Inserting  in  equation  (82)  the  number  of  leaves  figures  out  to 
5.1  X  425  X293 


=  7.05 


28,000,000  X  5  X   2  X  0.3003 
Therefore  seven  leaves  would  be  used.  - 

Comparison  of  Spring  Types. — The  load  on  each  end  of  a  half 
elliptic  spring  is  generally  denoted  by  P  and  the  half  length  by  /. 
The  total  load  on  the  spring  then  is 

W  =  2  P 

and  this  is  the  reaction  on  the  support,  if  we  neglect  the  weight 
of  the  spring  itself.  Now  suppose  the  same  spring  to  be  used  as  a 
floating  cantilever.  The  reaction  on  the  support  is  the  same  as 
before,  viz.,  2  P,  but  in  this  case  the  whole  load  comes  on  one  end 
of  the  spring.  The  reactions  at  the  middle  and  the  forward  end 
of  the  spring  can  then  be  easily  found  by  taking  moments  (Fig. 
352)  ;  they  are  4  P  and  2  P  respectively.  Hence,  since  the  load 


FIG.  352. 


at  each  free  end  is  twice  as  great  as  in  the  case  of  the  half  elliptic, 
each  end  will  deflect  twice  as  much  with  relation  to  the  center 
and  the  stress  in  the  spring  will  be  twice  as  great. 

Stress  in  and  Deflection  of  Cantilever  Springs. — The  expres- 
sion for  the  unit  stress  in  a  half  elliptic  spring  is 

6  P  I         3  W  I 

^     

n  b  f         n  b  i~ 

and  since  the  stress  in  a  cantilever  spring  is  twice  as  great  we 
have  for  it 


SPRINGS.  513 

6  W  I 


*J 


M  b  f 

With  the  half  elliptic  spring  the  reduction  in  the  opening  of  the 
spring  is  the  same  as  the  lowering  of  the  frame,  but  this  is  not  the 
case  with  a  cantilever  spring.  Since  the  forward  end  is  constrained 
to  maintain  the  same  level  relative  to  the  middle,  the  deflection 
of  the  forward  half  will  result  in  a  slight  rotation  of  the  spring 
around  its  center  support  and  the  rear  half  will  deflect  twice  as 
much  with  relation  to  the  frame  as  it  does  with  relation  to  the 
middle  section.  Since  each  half  of  the  spring  deflects  twice  as 
much  as  a  corresponding  half  elliptic,  it  is  obvious  that  the  lower- 
ing of  the  frame  is  four  times  as  great  as  with  a  half  elliptic 
spring.  The  equation  for  the  deflection  of  a  half  elliptic  spring 
is 

(4.25  to  5.1)  P  F          (4.25  to  5.1)   W  ? 

E  n  b  f  2E  n  b  tz 

where  W  is  the  weight  supported  by  the  spring,  and  since  a 
cantilever  spring  deflects  four  times  as  much  under  a  given  load 
as  the  same  spring  used  as  a  half  elliptic,  the  deflection  of  a  can- 
tilever spring  is  evidently  given  by  the  equation 

(8.5  to  10.2)   W  P 

d  — 

E  n  b  t3 

It  is  obvious  that  since  a  certain  spring  gives  a  deflection  four 
times  as  great  when  used  as  a  cantilever  as  when  used  as  a  half 
elliptic  the  same  spring  could  not  satisfactorily  be  used  in  both 
ways  for  a  certain  definite  spring  load.  For  a  given  load  the 
cantilever  spring  would  have  fewer  and  thicker  leaves  and  be 
shorter  than  the  half  elliptic.  We  will  now  assume  springs  of 
the  two  types  respectively,  designed  for  the  same  load.  The 
stresses  in  the  material  should  be  the  same  in  each  case,  as 
should  the  deflection  under  load,  as  this  latter  factor  determines 
the  riding  qualities.  We  will  designate  the  dimensions  of  the 
cantilever  spring  by  means  of  primes.  The  weight  of  a  vehicle 
spring  is  closely  proportional  to  the  product  of  its  length,  width, 
number  of  leaves  and  thickness  of  leaves.  It  is  then  to  be  deter- 
mined what  is  the  relation  of  this  product  for  the  cantilever 
spring  to  that  for  the  half  elliptic  spring. 

Since  the  stresses  in  the  material  of  both  springs  must  be  equal 
3  W  I  6  W  I' 

n  b  f          n   V  C 


514  SPRINGS. 

and  since  the  deflections  are  the  same 

4.25  W  I3  8.5  W  I'3 


2E  n  b  t3          E  n'  b'  t'3 
From  this  we  get 
/3  4/'3 

=  -  - (83) 

n  b  f         n    b'  t'3 

We  may  similarly  simplify  the  equation  of  the  expression   for 
the  stress  and  get 

/  21' 


Squaring  n  b  f          n   b'  t''2 

r  4r- 

—  (84) 

n2  b2  t4  n'2  b'2  *" 

Dividing  equation  (83)  by  equation  (84)  we  gel 


n  b  f  n    b'  t'3 


4P 


n2  b2  f4  n'2  b'2  t'4 

which  when  reduced  gives 

nb  I  t  =  n  b'  I'  t' 

Hence  the  weight  of  a  cantilever  spring  will  be  the  same  as  that 
of  a  half  elliptic  if  the  deflections  under  load  and  the  stresses  in 
the  material  are  the  same,  respectively. 

The  same  relation  holds  between  any  other  classes  of  springs. 
With  the  same  weight  of  spring  material  stressed  to  the  same 
degree  the  deflection  per  100  Ibs.  is  the  same,  and  conesquently 
the  riding  qualities  should  be  the  same.  The  choice  of  spring 
types,,  therefore,  is  not  so  much  a  question  of  riding  qualities  de- 
sired as  of  convenience  in  mounting  and  of  the  use  of  springs  for 
purposes  other  than  body  suspension,  such  as  the  transmission 
of  the  driving  thrust  from  the  axle  to  the  frame  and  taking  up 
the  torque  reaction. 

Mountings  of  Cantilever  Springs. — As  originally  designed  the 
cantilever  spring  took  neither  the  driving  thrust  nor  the  torque 
of  the  rear  axle,  a  pair  of  links  from  each  side  of  the  frame  to 
the  axle  serving  this  purpose.  The  rear  end  of  the  spring  rested 
on  a  roller  mounted  underneath  the  axle  housing.  Thus  the  axle 
was  securely  tied  to  the  frame,  and  breakage  of  the  springs  would 
not  cause  it  to  come  adrift.  Floating  cantilever  springs  in  sev- 
eral instances  are  used  to  take  the  driving  thrust.  In  one  con- 


SPRINGS. 


515 


struction  the  rear  end  of  the  spring  is  secured  to  the  spring  perch 
by  means  of  a  pressure  block  of  special  design,  as  illustrated 
in  Fig.  353,  and  clips.  In  another  design  a  bolt  is  passed  through 
the  end  of  the  master  leaf  and  the  rear  flange  of  the  spring  perch, 
and  a  clip  over  two  or  more  leaves  and  through  the  front  flange 
of  the  perch. 


o 


(    (     C 


)  )  )    ) 


FIG.  353.— WESTCOTT  CANTILEVER  SPRING. 

The  Hotchkiss  drive  is  also  being  used  on  commercial  vehicles 
•and  in  this  application  of  necessity  requires  particularly  rugged 
construction.  In  Fig.  354  is  shown  the  construction  of  the  Per- 
fection Spring  Company,  which  embodies  what  is  referred  to  as 
a  three  point  shackle.  The  shackles  are  mounted  on  a  spindle 
extending  from  a  bracket. 


i 

1 

1 

IT 

•  j 

1 

1  j-  J 

J  LL 

^=i 

JU 

FIG.  354.— PERFECTION  THREE  POINT  SHACT-T-. 


516 


SPRINGS. 


The  master  leaf  of  the  spring  is  formed  with  an  eye  surround- 
ing a  bolt  extending  from  this  bracket.  The  second  leaf  is  formed 
with  an  oblong  eye  through  which  passes  a  bolt  carried  in  the 
shackles  and  another  bolt  carried  by  the  shackles  ties  the  four 
longest  leaves  together  as  it  were. 

In  order  that  the  springs  may  be  able  to  protect  the  car  frame 
and  body  from  road  shock,  adequate  clearance  must  be  allowed 
between  the  frame  and  axles.  This  clearance  should  be  slightly 
greater  than  the  total  deflection  of  the  spring  under  dead  load. 
If  the  clearance  is  thus  limited  the  spring  can  never  be  stressed 
to  more  than  a  little  over  twice  its  normal  stress,  so  that  danger 
of  breakage  is  almost  eliminated  if  the  elastic  limit  is  from  2.5 
to  three  times  the  normal  stress.  A  rubber  bumper  is  usually 
attached  to  the  spring  at  the  centre  which  eliminates  shock  if 
the  spring  closes  up  completely. 

Centre  Bolts  and  Centre  Bands  —  The  separate  leaves  of 
leaf  springs  are  held  together  by  means  of  a  centre  bolt  and  nut. 
An  objectionable  feature  of  the  centre  bolt  is  that  it  materially 
weakens  the  spring,  and  breakages  through  the  centre  bolt  holes 
are  not  rare.  Some  spring  makers  have  attempted  to  overcome 
this  defect  by  using  in  place  of  the  centre  bolt  a  pair  of  beads 
formed  on  the  spring  leaf  at  its  centre,  nesting  in  depressions  in 
the  leaf  below.  While  this  does  not  hold  the  leaves  together,  it 
keeps  them  in  their  proper  relative  positions  longitudinally  as 
well  as  transversely.  However,  the  use  of  centre  bolts  is  well 
nigh  universal  and  the  S.  A,  E.  Standards  Committee  on  Springs 
has  recommended  the  following  sizes  for  these: 


FIG.  355.—  CENTRE  BOLT. 


Pleasure  cars  — 
Inches. 

A. 
Inches. 
5-16 

B 
Inches 

C. 

Inches. 

2  54  to  2  yi                  

^ 

Va 

J4 

Commercial    cars  — 

2       . 

.    5-i6 

M 

2y4  to  2y2    .......................  .    ^  H  54 

3  to  3y2   .........................  7-16  M  X 

4  to  4%    ........................     **  54  H 

The  bolts  are  to  have  S.  A.  E.  standard  threads,  and  hexagonal 

nuts  are  usually  employed.     Where  two  beads  or  nibs  are  used 


SPRINGS. 


517 
inch  diameter 


the  committee  recommends  that  they  be  made  of 
and  spaced  at  94  inch  centre  distances. 

Heavy  truck  springs  are  held  together  by  shrunk  centre  bands, 
as  shown  in  Fig.  356.  These  are  made  of  very  soft  iron  and  of 
the  following  dimensions  (according  to  the  Springs  Division  of 
the  S.  A.  E.  Standards  Committee)  : 


FIG.  356. — CENTRE  BAND. 


Load  Capacity 

of  Truck, 

Tons. 


A, 

Inches. 


H 


B, 

Inches. 


25* 

3 
3 


Spring  Arch. — Spring  leaves  are  made  from  rolled  stock,  and 
after  they  have  been  cut  to  the  right  length  are  tapered  and  bent 
to  form  an  arc  of  a  circle.  That  is  to  say,  the  majority  of 
springs,  which  are  said  to  have  a  true  sweep,  are  thus  bent ; 
truck  springs  are  occasionally  given  a  double  sweep,  the  ends 
curving  in  the  opposite  direction  to  the  middle  portion.  The 
difference  between  true  sweep  and  double  sweep  springs  is  largely 
one  of  appearance.  In  a  half  elliptic  spring  the  distance  between 
a  line  joining  the  centres  of  the  eyes  and  the  bottom  of  the 
shortest  leaf  (or  the  top  of  the  main  leaf)  is  known  as  the  arch. 
It  is  appare  it  that  the  necessary  arch  is  dependent  upon  the 
clearance  required  under  full  dead  load  and  on  the  design  of  the 
spring  brackets  and  frame.  A  relatively  small  arch  is  preferable, 
because  with  it  a  certain  increase  in  load  will  give  a  greater 
deflection.  This  can  easily  be  seen  by  reference  to  Fig.  357. 
The  bending  moment  at  a  distance  /  from  the  spring  eye  is  equal 
to  P  I  cos  a,  and  this  is  a  maximum  when  a  =  O,  that  is,  when 
the  spring  is  straight.  However,  some  arch  is  generally  neces- 
sary in  order  to  insure  the  required  clearance  when  the  spring  is 
under  load.  As  the  value  of  the  cosine  does  not  drop  much 


SPRINGS. 


FIG.  357. — DIAGRAM  SHOWING  EFFECT  OF  ARCH  ON  DEFLECTION. 

below  unity  for  the  first  10  degrees,  this  does  not  have  much 
effect  on  the  deflection.  Foreign  pleasure  cars  are  sometimes 
provided  with  nearly  flat  springs. 

Clips  and  Spring  Perches. — Half  elliptic  and  quarter  elliptic 
spring  members  are  secured  to  the  spring  seats  or  perches  by  means 
of  box  clips.  These  are  made  of  very  low  carbon  steel,  which  will 
not  easily  become  brittle  under  vibration,  or  preferably  of  nickel 
steel.  The  shank  is  made  of  a  diameter  equal  to  one-quarter  the 
spring  width  and  is  cut  with  an  S.  A.  E.  standard  screw  thread. 
Hexagonal  head  nuts  are  used  on  these  clips,  which  can  be 
locked  by  means  of  spring  washers,  check  n..ts  or  cotter  pins. 
Generally  the  ends  of  the  shanks  are  slightly  upset,  so  the  nuts 
cannot  be  lost.  The  distance  between  the  two  clips  is  made  as 
small  as  the  design  of  the  spring  saddle  permits,  because  that 
part  of  the  spring  between  clips  is  inactive ;  it  is  generally  about 
1.5  times  the  width  of  the  spring.  A  pad  of  some  soft  material 
has  to  be  placed  between  the  spring  and  its  seat.  Leather  and 


FIG.  358.— Box  CLIP. 


SPRINGS. 


519 


wood  have  been  used,  but  the  best  results  are  obtained  with  two 
Jayers  of  8  ounce  duck  soaked  in  white  lead.  Fig.  358  shows  a 
box  clip  fitted  in  place.  However,  heavy  washers  are  now  used 
and  the  units  are  made  two  diameters  high. 

If  the  rear  springs  take  up  the  torque  or  brake  reaction  their 
perches  must  be  securely  fastened  to  the  axle  housings  by  rivet- 
ing or  otherwise.  Else  the  perches  swivel  on  the  axle  tube 
between  shoulders,  as  shown  in  Fig.  359  at  A.  The  perch  is  made 
in  two  parts,  joined  in  a  horizontal  plane  and  held  together  by 
two  square  head  bolts  whose  heads  are  sunk  into  the  spring  seats. 


FIG.  359. — SPRING  PERCHES. 

Some  designers  form  the  upper  part  of  the  spring  perch  with 
lugs  to  which  the  radius  rod  connects. 

Undoubtedly  the  best  mounting  for  a  spring  perch  is  that  illus- 
trated in  Fig.  359  at  B.  A  sleeve  with  a  spherical  outside  sur- 
face is  riveted  to  the  axle  tube,  and  the  perch,  which  is  made  in 
two  parts,  is  bored  out  to  fit  this  sphere,  so  as  to  give  a  uni- 
versal connection.  With  the  ordinary  form  of  spring  mounting 
if  one  rear  wheel,  say,  rises  over  an  obstruction,  both  rear  spring; 
are  subjected  to  torsional  strains,  which  they  are  ill  adapted  tc 
withstand,  and  this  is  avoided  by  using  spring  perches  with 
spherical  seats. 


520 


SPRINGS. 


FIG.  360.— TIM  KEN  ADJUSTABLE  SPRING  PERCH. 

Front  and  rear  solid  axles  usually  have  the  spring  seats 
forged  integral  with  them.  However,  a  great  many  motor  truck 
axles  are  manufactured  by  parts  makers,  and  it  is  then  practically 
impossible  to  provide  in  the  dies  for  integral  spring  seats,  be- 
cause of  variations  in  the  width  of  the  frame  in  different  designs 
of  trucks  of  substantially  the  same  capacity.  Fig.  360  illustrates 
the  manner  in  which  the  Timken-Detroit  Axle  Company  get 
around  this  difficulty.  A  spring  block  is  placed  on  top  of  the 
axle  and  the  spring  secured  in  place  by  means  of  two  clips  or 
four  bolts  whose  lower  ends  pass  through  cleats  on  the  under 
side  of  the  axle. 

Instead  of  having  the  box  clips  bear  directly  upon  the  spring 
leaves,  a  pressure  block  is  sometimes  inserted  between  them.  As 


FIG.  361.— SPRING  PRESSURE  BLOCK. 


SPRINGS. 


521 


shown  in  Fig.  361,  this  is  made  with  grooves  for  the  clips,  with 
a  hole  or  socket  for  the  head  of  the  centre  bolt  and  with  a 
curved  under  surface.  This  curved  under  surface  obviates  local- 
ization of  the  stress  at  the  end  of  the  spring  seat  and  renders  the 
whole  length  of  the  spring  available  for  elastic  deflection. 

Rebound  Clips  and  Reverse  Leaves. — When  the  wheel 
strikes  an  obstacle  in  the  road  the  spring  near  it  is  compressed, 
whereby  energy  is  stored  up.  Immediately  after  the  compression 
has  ceased  the  spring  distends  again,  and  if  the  blow  to  the 
wheel  was  a  heavy  one  the  rebound  will  carry  the  body  far 
beyond  its  original  position  of  rest  relative  to  the  axle.  The 
main  leaf  of  the  spring  will  thereby  be  curved  in  the  reverse  di- 
rection, and  as  it  is  not  supported  by  the  other  leaves  in  this 
direction,  it  is  apt  to  be  stressed  beyond  the  elastic  limit  by  the 
rebound. 


FIG.  362. — REBOUND  CLIP. 

There  are  several  methods  of  preventing  such  injury  to  the 
main  leaf.  The  most  common  consists  in  the  use  of  rebound  clips 
by  which  part  of  the  load  will  be  transferred  during  sharp  re- 
bounds from  the  main  leaf  to  the  second  and  third  leaves.  As 
shown  in  Fig.  362  the  rebound  clip  is  preferably  riveted  to  the 
end  of  the  shortest  leaf  which  it  surrounds,  and  a  tubular  spacer 
is  slipped  over  the  bolt  to  prevent  the  leaves  being  clamped 
between  the  ends  of  the  U-shaped  clip,  whereby  their  free  play 
under  ordinary  running  conditions  would  be  hampered.  There 
is  also  another  simpler  form  of  clip,  known  as  the  clinch  clip, 
which  is  simply  a  piece  of  flat  steel  bent  into  rectangular  form, 
with  the  joint  at  the  middle  of  one  of  the  long  sides.  This  form 
of  clip  is  used  mainly  near  the  spring  eyes,  which  hold  it  in 
position. 

Another  method  of  limiting  the  rebound  consists  in  placing  a 
couple  of  reversely  curved  leaves  on  top  of  the  main  leaf,  as  illus- 
trated in  Fig.  363.  These  reinforce  the  main  leaf  during  the 
rebound  and  prevent  its  breakage.  Finally,  quite  a  number  of 
makers  now  connect  the  frame  at  the  rear  with  the  axle  tube  by 
rebound  straps,  one  on  each  side,  which  limit  the  rebound  motion. 


522 


SPRINGS. 


Alignment— Although  the  clips  at  the  centre  of  a  spring  tend 
to  hold  the  leaves  in  alignment,  they  alone  are  not  sufficient,  and 
some  means  of  preventing  lateral  motion  of  the  leaves  must  be 


FIG.  363. — REVERSE  LEAVES. 

provided  at  their  ends.  One  of  the  most  common  plans  is  to 
raise  a  central  longitudinal  rib  on  the  leaves  for  a  certain  dis- 
tance from  the  end,  the  rib  on  one  leaf  entering  a  corresponding 
gutter  on  the  next.  This  method  is  quite  successful,  but  un- 
fortunately it  does  not  permit  of  the  use  of  clips  on  the  leaves. 
Another  widely  followed  plan  consists  in  providing  the  ends  of 
the  leaves  with  lips,  by  drawing  out  the  leaf  stock  laterally  in  the 
forge  and  bending  the  lips  at  right  angles,  as  shown  in  Fig.  364. 
A  third  method  consists  in  slotting  the  end  of  the  leaf  longi- 
tudinally and  raising  a  nib  on  the  leaf  below  it.  The  first  and 
third  methods  are  illustrated  in  Fig.  365,  which  figure  shows  all 
of  the  different  spring  points  in  use.  The  most  common  forms 
of  points  are  the  egg-shaped ;  round,  short  French ;  round  end ; 
slot  and  bead;  ribbed  and  square,  and  tapered  points. 

Spring  Eyes,  Bolts  and  Shackles — The  eyes  are  either 
turned  in  or  out,  or  are  in  line  with  the  main  leaf,  as  illus- 
trated in  Fig.  366  at  A,  B  and  C,  respectively.  In-turned  eyes 
are  the  most  advantageous,  as  they  are  easier  to  make  than 
the  central  eyes,  and  there  is  less  danger  of  their  opening  up 
under  the  pressure  of  road  shocks  than  with  out-turned  eyes. 
According  to  S.  A.  E.  specifications,  the  width  of  the  leaves 
at  the  eyes  must  be  within  0.005  inch  of  the  nominal  size.  In 


FIG.  364. — SPRING  LIPS. 

all  high  grade  work  the  spring  eyes  are  bushed  with  either 
phosphor  bronze  or  steel.  In  case  the  latter  material  is  used 
a  seamless  steel  tube  cut  to  the  right  length  is  forced  into  the 
eye  and  reamed  out.  With  phosphor  bronze  bushings  the  bolt 


SPRINGS. 


523 


FIG.  365.— SPRING  LEAF  POINTS. 

preferably  should  be  case  hardened  and  ground.  The  object 
of  bushing,  of  course,  is  to  provide  means  for  readily  renew- 
ing the  wearing  surface  when  that  becomes  necessary.  The 
S.  A.  E.  committee  recommends  bushings  of  one-eighth-inch 
wall  thickness. 

Truck  springs  occasionally  are  provided  with  elongated 
eyes,  known  as  box  eyes,  which  slide  on  rollers  over  the 
spring  bolts;  they  are  also  made  without  eyes  at  either  one 
or  both  ends,  the  ends  sliding  in  combined  wear  plates  and 
guides. 

Some  means  must  be  provided  for  effectively  lubricating 
the  shackle  bolts,  as  they  are  working  continuously  and  will 
quickly  wear  out  if  they  are  allowed  to  remain  dry.  Small 
grease  cups,  with  one-eighth  inch  pipe  threaded  stems,  are 


FIG.  366.— SPRING  EYES. 

screwed  into  the  heads  of  these  bolts,  or  the  bolts  are  made 
with  integral  grease  cups.  Both  methods  are  illustrated  in 
Fig.  367.  In  the  cheaper  cars  oil  cups  are  provided  instead 
of  grease  cups,  or  even  only  oil  holes.  In  platform  springs 


524 


SPRINGS. 


the  side  springs  are  connected  to  the  cross  springs  by  means 
of  double  or  universal  shackles,  as  illustrated  in  Fig.  368. 
These  should  be  made  as  short  as  possible,  especially  in  the 
case  of  pleasure  cars,  as  there  is  always  an  unpleasant  sway- 
ing of  cars  fitted  with  platform  springs  when  driven  at  speed, 
which  is  one  of  the  chief  reasons  why  platform  springs  were 
largely  given  up  for  three-quarter  elliptic  on  pleasure  cars. 
These  springs  are  now  used  to  quite  an  extent  on  motor  trucks 
of  the  speedier  class.  In  this  class  of  work  the  double  shackle 
usually  consists  of  two  substantially  U-shaped  members  which 
are  hooked  together,  the  same  as  used  on  horse  trucks,  so 
there  are  only  two  pivot  joints  to  each  double  shackle. 


FIG.  367. — SPRING  SHACKLES  AND  SHACKLE  BOLTS. 

The  distance  apart  of  the  spring  brackets  should  be  fixed 
so  that  when  the  spring  carries  its  normal  load  the  shackles 
stand  vertically,  whether  they  be  in  tension  or  compression. 
This  arrangement  gives  the  greatest  assurance  that  the  shackles 
will  never  come  into  a  position  parallel  to  the  ends  of  the  main 
leaf  in  which  the  spring  is  locked.  To  prevent  the  reversal  of 
shackles  due  to  excessive  rebound  they  are  now  often  made 
of  substantially  U-shape,  as  shown  in  Fig.  369,  which  limits 
their  angular  motion.  These  are  known  as  non-reversible 
shackles. 

Inclined  Springs. — Front  half  elliptic  and  full  elliptic  springs 
occasionally  are  set  so  that  the  line  connecting  the  two  spring 
eyes  is  not  horizontal,  but  slants  upward  in  the  forward  direc- 
tion. The  reason  for  this  is  that  the  direction  of  the  worst 
shocks  on  the  spring  is  not  vertical  but  slightly  inclined  to 
the  rear,  and  it  is,  of  course,  advantageous  to  have  the  direc- 
tion of  heavy  shocks  coincide  with  the  direction  of  spring 


SPRINGS. 


525 


FIG.  368. — DOUBLE  SHACKLES  FOR  PLATFORM   SPRINGS. 

play.  This  inclination  can  be  obtained  with  semi-elliptic 
springs  by  placing  the  eye  of  the  rear  bracket  slightly  lower 
than  the  eye  of  the  front  bracket,  and  with  full  elliptic  springs 
by  suitably  inclining  the  seat  of  the  spring  bracket  on  the 
frame.  Full  elliptic  and  three-quarter  elliptic  springs  are 
sometimes  clipped  to  the  under  side  of  the  axle  in  order  to 
lower  the  frame,  and  are  then  said  to  be  underslung. 

Torsion  and  Thrust  on  Spring — In  a  few  cars  the  torsion 
due  to  the  rear  axle  drive,  the  driving  thrust  of  the  rear 
wheels,  and  the  torsion  and  thrust  due  to  the  action  of  the 


FIG.  369. — NON-REVERSIBLE  SHACKLE. 


526 


SPRINGS. 


FIG.  370. — AUXILIARY  TRUCK  SPRING. 

brakes  are  taken  up  by.  the  springs.  Since  only  the  main 
leaf  connects  the  axle  to  the  frame  it  is  on  this  leaf  that  mos» 
of  the  extra  strain  due  to  these  forces  comes.  This  makes  it 
necessary  to  use  leaves  of  comparatively  little  arch  and  to 
provide  spring  clips.  Engineering  opinion  regarding  this  practice 
is  divided;  some  regard  it  as  crude  and  unsatisfactory,  while 
others  claim  to  be  highly  advantageous. 

Auxiliary  Springs — Auxiliary  or  jack  springs  are  used  on 
motor  trucks  to  take  up  part  of  the  load  when  the  truck  is 
heavily  loaded.  They  are  generally  secured  to  the  top  of  the 
half  elliptic  springs,  and  their  ends  come  in  contact  with 
wear  plates  on  the  under  side  of  the  frame  side  rails  after 
the  main  leaves  have  compressed  a  certain  amount.  Another 
plan  is  to  secure  the  jack  spring  to  the  under  side  of  a  frame 
cross  member  and  let  its  ends  bear  against  wear  plates  on 
the  rear  axle.  (Fig.  370.) 

Lubrication— Although  friction  between  leaves  is  desirable 
to  an  extent,  because  it  dampens  the  rebound,  yet  it  is  neces- 
sary to  keep  the  leaves  lubricated  where  they  bear  one  against 
another.  The  common  plan  is  to  pry  the  leaves  apart  in 
some  manner  and  introduce  lubricant  between  them  with  a 
table  knife.  To  enable  the  leaves  to  hold  the  lubricant  they 
are  now  rolled  of  the  section  shown  in  Fig.  371,  so  as  to 
form  a  grease  retaining  space  between  them.  Lubrication  of 


FIG.  371. 


SPRINGS.  527 

the  leaves  is  necessary  mainly  because  without  it  there  is  an 
objectionable  squeak,  though,  of  course,  it  also  results  in 
reducing  frictional  losses. 

Some  makers  in  designing  their  springs  take  account  of  the 
fact  that  the  torque  reaction  of  the  motor  increases  the  load 
on  the  springs  on  the  right  side  of  the  car  and  decreases  that 
on  the  springs  on  the  left  side  (for  a  motor  rotating  right 
handedly)  by  making  the  right  hand  springs  slightly  stiffer, 
but  this  effect  is  usually  neglected. 


CHAPTER  XIX. 


ROAD  WHEELS. 

There  are  essentially  three  types  of  wheels  used  on  motor 
cars,  viz.,  artillery  wood  wheels,  which  are  used  on  the  great 
majority  of  all  vehicles;  steel  wire  wheels,  which  are  used  on 
some  pleasure  cars,  and  cast  steel  wheels,  which  are  used  on 
lieavy  trucks.  Disc  wheels  made  from  pressed  steel  are  also 
being  used,  but  only  in  rare  instances. 

Artillery  Wheels. — Wood  artillery  wheels  consist  of  a  set 
of  spokes  turned  from  some  very  tough  wood,  generally  hickory, 
which  are  clamped  at  their  inner  end  between  flanges  on  a  metal 
hub  and  at  their  outer  end  are  tenoned  into  a  wooden  felloe, 
which  later  is  surrounded  by  a  steel  band  or  ring.  The  spokes 
are  turned  to  an  elliptic  section,  and  great  pains  must  be  taken  to 
get  the  fibre  to  run  exactly  in  the  direction  of  the  spoke  length. 
The  spoke  billets  must  be  split  and  not  sawed. 

Spoke  and  Felloe  Material. — The  spokes  and  felloes  of  ar- 
tillery wheels  are  made  from  well  seasoned  or  kiln  dried  hickory, 
which  is  used  because  it  combines  strength,  toughness  and  elastic- 
ity in  the  highest  degree.  Hickory  grows  in  many  parts  of  the 
United  States,  but  the  best  qualities  are  said  to  come  from  the 
Ohio  Valley  and  from  the  northern  portions  of  the  country. 
Second  growth  stock  and  stock  from  the  lower  portion  of  small 
trees  yield  the  best  parts.  The  wood  should  preferably  be  cut 
when  all  the  sap  is  out  of  the  tree,  which  makes  the  cutting  sea- 
son in  the  southern  part  of  the  country  exceedingly  short.  Hic- 
kory is  mostly  cut  by  mill  men  operating  portable  saw  mills,  who, 
when  the  supply  in  a  certain  district  is  exhausted,  move  their 
plant  to  another  part.  These  mill  men  sell  their  stock  to  the 
wheel  makers. 

Wheel  Diameters. — It  is  now  the  universal  custom  in  pleasure 
car  design  to  use  wheels  of  the  same  diameter  in  front  and  rear, 
because  with  equal  sized  front  and  rear  tires  only  a  single  spare 
need  be  carried.  The  most  common  wheel  diameters  for  pleasure 

528 


ROAD  WHEELS.  5^ 

cars  are  32,  34  and  36  inches.    Wheel  diameters  vary  with  the 
wheelbase  substantially  as  follows : 

Inches. 

Less  than   100  inch   wheelbase 30 

100  to  110  inch  wheelbase 32 

110  to  120  inch  wheelbase 34 

115  to  135  inch  wheelbase : 36 

It  will  be  noticed  that  the  wheelbase  ranges  for  34  inch  and 
36  inch  wheels  overlap.     For  wheelbases  between  110  and  120 


FIG.  372. — SPOKE  AND  FELLOE  ASSEMBLY  OF  PLEASURE  CAR  WHEEL. 


inches  36  inch  tires  are  used  on  the  more  expensive  cars  and  34 
inch  on  the  lower  priced.  Outside  wheel  diameters  are  always 
expressed  in  even  numbers  of  inches,  except  when  the  so-called 
mongrel  tires  are  used ;  that  is,  a  tire  of  a  given  width  on  a  rim 
designed  for  a  tire  one-half  inch  narrower.  A  few  makers  have 
used  wheels  of  40  and  42  inches  diameter,  but  such  cases 
are  rare.  One  reason  for  using  such  large  wheels  is  the  desire 


530 


ROAD  WHEELS. 


to  secure  ample  ground  clearance  in  underslung  cars.  Large 
wheels,  of  course,  improve  the  riding  qualities  of  the  car  and  add 
to  the  life  of  the  tires,  but  these  advantages  are  at  least  partly 


w 


offset  by  their  increased  cost.  They  also  greatly  increase  the 
stress  in  the  axles,  as  the  leverage  of  a  lateral  shock  to  the 
wheel  is  proportional  to  the  wheel  diameter. 


ROAD  WHEELS.  531 

In  motor  truck  work  34  and  36  inch  wheels  are  used  almost 
exclusively,  irrespective  of  size,  except  that  the  rear  wheels  of 
5-ton  and  over  trucks  sometimes  are  made  as  large  as  42  inches 
in  diameter.  In  this  connection  it  may  be  pointed  out  that  in 
motor  trucks  the  front  wheels  are  frequently  made  of  somewhat 
smaller  diameter,  since,  until  recently,  solid  rubber  tires  were  not 
made  so  they  could  be  interchanged  by  the  driver,  and,  therefore, 
there  v:as  no  advantage  in  interchangeable  front  and  rear  tires. 

The  diameter  of  the  wood  wheel  is  less  than  the  nominal 
wheel  diameter  by  twice  the  height  of  the  tire  and  rim.  For  solid 
tired  wheels  the  dimensions  have  been  standardized  by  the 
S.  A.  E.  and  the  standard  specifications  will  be  found  in  the  ap- 
pendix to  this  volume.  Standardization  of  pneumatically  tired 
wheels  along  similar  lines  is  now  under  way. 

Number  of  Spokes — Front  wheels  of  pleasure  cars  are  made 
with  either  10  or  12  spokes,  rear  wheels  of  pleasure  cars  with  12 
spokes.  For  motor  trucks  the  numbers  of  spokes  are  made  sub- 
stantially as  follows: 

Load  Capacity.                                                                     Front.  Rear. 

One    ton    or    less 12  12 

il/2    to    2l/2    tons 12  14 

2l/2    to    4l/2    tons 14  14 

Over    45^    tons 14  16 

Proportions  of  Spokes — Until  quite  recently  it  was  the  uni- 
versal practice  to  make  spokes  of  an  elliptic  section,  the  width 
of  the  spoke  averaging  three-fourths  its  depth  in  the  direction  of 
the  wheel  axis.  Lately,  however,  spokes  of  square  or  rectangular 
section  have  come  into  extensive  use  for  truck  wheels  and  bid 
fair  to  oust  the  elliptic  spoke  entirely  for  that  purpose,  since  the 
rectangular  spoke  is  stronger  in  proportion  to  weight  than  the 
elliptic  spoke.  The  width  of  the  spoke  is  generally  made  con- 
stant from  end  to  end,  but  the  depth  or  thickness  (dimension  in 
the  direction  of  the  wheel  axis)  tapers  about  l/%  inch  from  hub 
to  felloe.  However,  in  heavy  truck  wheels,  which,  on  account  of 
their  dual  and  even  triple  tires,  require  very  wide  felloes,  the 
thickness  of  the  spoke  is  sometimes  made  increasing  from  the 
hub  toward  the  felloe.  Improved  turning  lathes  have  recently 
been  introduced  in  wheel  manufacture  which  allow  of  obtaining 
two  opposite  tapers  in  one  operation. 

Ine  tenons,  which  are  forced  into  holes  drilled  in  the  felloes, 
are  made  equal  in  diameter  to  about  one-half  the  depth  of  the 
spoke.  One  wheel  maker  says  that  they  should  be  made  of  such 
length  that  they  extend  entirely  through  the  felloe  and  bear  up 


532  ROAD  WHEELS. 

against  the  steel  band.  This  causes  the  pressure  of  the  load  to 
be  transferred  directly  from  the  spokes  to  the  steel  band  and 
prevents  splitting  of  the  felloe  through  the  tenon  holes.  The 
length  of  the  mitre  or  head  of  the  spoke  held  between  flanges 
should  be  at  least  1.25  times  the  depth  of  the  spoke.  The  throat 
of  the  spoke,  or  that  portion  intermediate  between  the  barrel 
and  the  mitre,  is  drawn  to  a  radius  of  about  2  inches  and  so 
that  the  throat  circles  of  adjacent  spokes  intersect  at  ^  inch 
from  the  hub  flange  circle,  while  the  curved  edge  of  the  face  of 
the  mitre  comes  l/%  inch  from  the  hub  flange  circle. 

Spoke  Dimensions. — It  is  found  that  the  greatest  strain  on 
artillery  spokes  is  the  result  of  lateral  forces  due  to  skidding. 
The  wheels  must  be  made  strong  enough  to  withstand  any  such 
shocks  which  are  proportional  to  the  weight  upon  them.  The 
resistance  of  the  wheel  to  withstand  lateral  shocks  is  proportional 
to  the  number  of  spokes,  to  the  section  modulus  of  the  spoke  and 
inversely  to  the  diameter  of  the  wheel.  That  is, 

n  Z 

W. 

D 

Calling  the  depth  or  thickness  of  the  spoke  (dimension  between 
flanges)  d  and  the  width  b,  the  section  modulus  of  an  oval  spoke 
b  d2  b  d'2 

is   approximately  and  that  of   a   rectangular   spoke   . 

10  6 

Hence  n  b  tf 

W 

D 

But  b  varies  substantially  in  proportion  to  d,  and  therefore  we 
may  write 

n  d* 

W 

and  D 


n 

Also,  since  it  is  customary  to  use  spokes  of  the  same  size  for 
front  and  rear  wheels,  notwithstanding  the  fact  that  they  carry 
different  maximum  loads,  we  will  take  for  W  the  total  weight 
of  the  car  and  load.  The  author's  data  shows  that  the  average 
value  of  c  in  pleasure  car  practice  is  14.  Hence 

1     \W  D 

d  =  r4S/— (85) 

In  the  case  of  truck  wheels,  since  the  ratio  of  width  to  thick- 
ness of   spokes   varies  considerably,   it  is  best  to   introduce  the 


ROAD  WHEELS. 


533 


width  in  the  formula.  Also,  a  separate  equation  should  be  given 
for  spokes  of  rectangular  section.  Since  the  spokes  of  front 
and  rear  wheels  are  often  made  of  different  thicknesses,  it  is 
best  to  introduce  in  the  formula  the  weight  w  on  the  front  and 
rear  axles,  respectively.  The  author  finds  that  in  modern  prac- 
tice 


ivD 

1,000 


for  oval  spokes  ................................  (86) 


and 


w  D 
1,500 


for  rectangular  spokes  ......................  (87) 


FIG.  374.— PLEASURE  CAR  FRONT  HUB. 

Wheel  Hubs — The  hubs  of  artillery  wheels  are  made  either 
of  cast  steel  or  of  malleable  iron.  Fig.  374  shows  a  typical 
design  of  pleasure  car  front  hub,  and  Fig.  375  a  design  of  truck 
rear  hub.  The  general  form  of  the  hubs  is  largely  determined  by 
the  dimensions  of  the  bearings  and  their  necessary  distance 
apart.  The  outer  hub  flange  is  generally  made  integral  with  the 
hub  casting,  while  the  inner  one  is  free,  being  slipped  over  a 


534 


ROAD  WHEELS. 


machined  cylindrical  surface  so  as  to  be  accurately  guided. 
Some  manufacturers  round  the  inner  inside  edge  of  the  movable 
flange,  but  wheel  makers  say  that  this  practice  is  to  be  con- 
demned. If  the  flange  has  a  fairly  sharp  corner  and  meets  the 
hub  barrel  at  90  degrees  the  clamped  surface  of  the  spoke  mitre 
is  considerably  longer  and  the  spoke  is  held  so  much  more  se- 
curely. Nearly  all  trouble  with  artillery  wood  wheels  is  due  to 
shrinkage  of  the  spokes,  causing  looseness  in  the  hubs. 


FIG.  375.— TRUCK  REAR  HUB. 


There  is  much  variety  in  respect  to  the  number  of  flange 
bolts  used,  and  the  manner  of  locating  them.  The  most  extensive 
practice  is  to  use  one  bolt  for  every  two  spokes  and  to  place  it 
between  the  mitres  of  adjacent  spokes.  However,  some  manu- 
facturers use  a  bolt  for  each  spoke,  placing  it  between  adjacent 
spokes,  while  still  others  pass  it  right  through  the  centre  of  the 
mitre. 

Securing  Sprockets  and  Brake  Drums— Where  a  brake 
drum  is  secured  to  the  rear  wheel  it  is  sometimes  fastened  only 
by  the  regular  hub  flange  bolts,  the  pressed  steel  drums  serving 
also  as  the  loose  flange  of  the  hub.  In  this  case,  naturally,  the 


ROAD  WHEELS. 


535 


integral  flange  is  made  of  considerable  diameter  and  the  flange 
bolts  are  placed  as  far  out  as  possible.  Other  designers,  how- 
ever, use  two  circles  of  bolts,  one  passing  through  the  integral 
flange,  spoke  and  brake  drum,  and  the  other,  outer  one,  through 
the  spoke  and  brake  drum  only.  In  the  latter  case  the  spokes 
are  generally  enlarged  where  the  bolts  pass  through  them,* as 
shown  in  Fig.  376  at  A.  Instead  of  securing  the  brake  drum 
by  means  of  bolts,  some  designers  provide  clips,  as  shown  in  the 
same  figure  at  B.  Where  brake  drums  are  directly  secured  to 
wheel  spokes  it  is  desirable  that  the  flat  of  the  spokes  at  the 
joint  with  the  drum  be  equal  to  the  greatest  width  of  the  spoke, 
as  otherwise  a  sharp  angle  is  formed  at  the  joint,  in  which  dirt 
collects. 


A/V\ 


FIG.  376. — BRAKE  DRUM  FASTENINGS. 


In  order  to  strengthen  the  spoke  assembly  at  the  centre  the 
Schwarz  Wheel  Company  makes  the  mitre  of  the  spokes  inter- 
locking, as  illustrated  in  Fig.  377,  and  some  other  manufacturers 
provide  keys  between  the  mitres  of  adjacent  spokes. 

Hub  Caps. — Wheels  are  held  in  place  on  the  axle  spindles 
by  nuts  on  the  ends  of  the  latter,  which  bear  against  the  inner 
race  of  the  outermost  anti-friction  bearing  and  which  are  locked 
against  unscrewing  by  split  pins  or  similarly  effective  means. 
However,  the  hubs  are  provided  at  their  outer  ends  with  screw 
caps,  in  order  to  retain  the  lubricant  in  the  bearing  and  exclude 
dust  and  grit,  as  well  as  for  the  sake  of  appearance.  These  hub 
caps  are  provided  with  a  comparatively  fine  thread,  and  screw 
up  against  a  shoulder  formed  on  the  hub  barrel,  the  thread  being 
either  on  the  inside  or  outside  of  the  barrel.  As  loss  of  hub 
caps  is  a  very  annoying  thing,  they  are  often  locked  by  the 


536 


ROAD  WHEELS. 


familiar  spring  wire  ring  locking  device,  while  the  hub  caps  of 
motor  trucks,  which,  on  account  of  the  greater  vibration  on  solid 
tired  vehicles,  are  particularly  apt  to  shake  loose,  are  sometimes 
made  with  a  small  drilled  lug  and  wired  to  one  of  the  spokes  to 
prevent  their  loss.  In  order  to  make  it  possible  to  conveniently 
remove  them,  the  hub  caps  of  pleasure  cars  are  generally  pro- 
vided with  a  hexagonal  outer  portion  to  which  a  monkey  wrench 
can  be  applied,  or  with  a  slotted  flange  taking  a  special  wrench. 
A  good  scheme  in  connection  with  large  truck  hub  caps  is  to  cast 
them  with  four  square  lugs  on  their  outer  plane  surface,  between 
which  a  pry  bar  can  be  inserted. 


FIG.  377.— SCHWARZ  INTERLOCKING  SPOKE. 

Owing  to  the  difficulty  of  unscrewing  a  cap  with  a  thread  3  to 
4  inches  in  diameter,  some  makers  secure  the  hub  caps  by  means 
of  cap  screw  bolts.  It  is  a  common  practice  to  cast  the  name  of 
the  manufacturer  or  his  trade  mark  on  the  hub  cap.  For  light 
cars  the  caps  are  sometimes  made  of  sheet  metal. 

Dished  Wheels — Front  wheels,  as  well  as  rear  wheels  of 
those  shaft  driven  cars  which  have  an  arched  rear  axle  are  gen- 
erally dished;  that  is,  the  spokes  are  set  at  an  angle  with  a  plane 
perpendicular  to  the  axis  of  the  wheel.  In  standard  American 
practice  the  dish  is  made  2  degrees.  This  must  be  provided  for 
in  turning  the  hub  flanges.  Dishing  greatly  adds  to  the  lateral 
strength  of  the  wheel,  because  it  distributes  the  stress  due  to  any 
lateral  shocks  over  a  considerable  number  of  spokes.  Wheel 
makers  who  have  been  accustomed  to  dished  wheels  all  their 
lives — these  wheels  being  used  exclusively  for  horse  vehicles — 


ROAD  WHEELS.  537 

also  maintain  that  dishing  adds  to  the  beauty  of  a  wheel.  The 
dish  of  the  spokes  and  the  set  or  camber  of  the  axle  should 
preferably  be  alike,  as  then  the  bottom  spokes,  which  carry  the 
load,  will  stand  vertical. 

Manufacture  of  Wheels — At  the  wheel  manufacturing  plants 
the  spoke  billets  and  felloe  strips  arrive  in  the  green  state,  and 
the  first  operation  consists  in  kiln  drying  them.  They  are  packed 
in  the  kiln,  which  is  now  generally  heated  by  steam,  and  the  best 
results  are  said  to  be  obtained  by  starting  with  a  low  heat, 
gradually  increasing  it  to  a  maximum  and  then  decreasing  it 
again.  After  this  process  has  been  completed  the  billets  for  the 
spokes  are  placed  in  eccentric  turning  machines  and  the  barrel 
portion  of  the  spokes  is  turned  substantially  to  size,  whife  the 
head  end  is  left  in  the  rough  state.  The  spokes  then  go  back 
for  another  drying  treatment  in  the  kiln,  after  which  the  head 
ends  are  mitred  and  faced,  and  the  spokes  are  equalized  and 
sanded. 

The  felloe  stock  as  it  arrives  from  the  saw  mill  is  steamed  in 
both  exhaust  and  live  steam,  and  is  then  bent  to  the  proper  curva- 
ture, after  which  it  is  placed  in  the  kiln  and  dried  for  from  20  to 
30  days.  Upon  the  completion  of  the  drying  treatment,  the 
felloes  are  planed,  bored,  rounded  and  sanded.  The  felloe  of  a 
wheel  is  always  made  in  halves,  and  the  next  operation  consists 
in  assembling  each  half  felloe  with  its  spokes,  the  tenons  of  the 
spokes  being  forced  into  the  felloe.  Next,  the  two  halves  of  the 
wheel  are  inserted  in  a  screw  press  and  forced  on  to  a  dummy 
hub.  They  are  then  equalized;  that  is,  reduced  to  the  same 
height,  and  the  wheel  is  then  reduced  to  the  proper  diameter  for 
the  steel  band.  The  latter  is  heated  before  being  applied  to  the 
felloe,  and  after  being  put  in  place  is  compressed  on  it  by  means 
of  an  hydraulic  press.  The  dummy  hub  is  then  taken  off  and 
the  wheel  is  sanded  and  primed  or  oiled,  and  the  hub  and  other 
metal  parts  are  fitted  to  it.  The  two  halves  of  the  felloe  are 
joined  together  by  means  of  steel  plates  extending  across  the 
joint  and  secured  to  the  felloes  by  bolts. 

Wire  Wheels — Wire  wheels  were  used  in  this  country  to  a 
considerable  extent  in  the  early  days  of  the  automobile,  but, 
probably  on  account  of  too  light  construction,  gave  a  great  deal 
of  trouble  and  were  soon  discarded.  They  were  reintroduced  by 
an  English  manufacturer  about  1908,  and  are  now  widely  used 
abroad,  and  also'being  taken  up  again  in  this  country.  The  chiet 
advantage  of  the  wire  wheel  is  that,  as  compared  with  a  wood 
artillery  wheel,  it  has  a  much  greater  lateral  strength  in  pro- 


538 


ROAD  WHEELS. 


FIG.  378.— SECTIONAL  VIEW  OF  RUDGE-WHITWORTH  WIRE  SPOKK 


ROAD  WHEELS.  539 

portion  to  its  weight.  This  makes  it  possible  to  use  wheels  of 
smaller  weight,  which  are  easier  on  tires,  and  some  comparative 
tests  made  by  the  London  Taxicab  Company  are  said  to  have 
shown  a  remarkable  tire  economy  in  favor  of  the  wire  wheel.  An 
objection  to  the  wire  wheel  is  that  it  is  not  as  easily  kept  clean 
as  an  artillery  wood  wheel. 


FIG.  379. — SIDE  VIEW  OF  WIRE  WHEEL. 

At  present  wire  wheels  are  generally  made  of  the  demountable 
type,  these  wheels  abroad  being  provided  with  a  hub  in  the 
form  of  a  comparatively  thin  steel  shell  formed  with  serrations 
on  its  inner  circumference,  which  is  slipped  over  the  regular 
hub  on  the  axle  and  secured  in  place  by  means  of  a  clamping 
nut.  The  Rudge-Whitworth  wheel,  illustrated  in  Fig.  378,  is  of 
this  type.  Such  a  wheel  serves  the  same  purpose  as  the  demount- 
able rim  generally  used  in  this  country,  one  or  more  complete 


540  ROAD  WHEELS. 

extra  wheels  being  carried  on  the  car,  and  in  case  a  tire  puncture 
or  other  tire  defect  is  suffered,  the  wheel  carrying  the  damaged 
tire  is  removed  and  one  of  the  spare  wheels  with  its  tire  already 
inflated  is  substituted  therefor.  In  the  McCue,  a  wire  wheel 
made  in  this  country,  the  hub  of  the  wheel  is  driven  by  a  num- 
ber of  pins  secured  into  a  flange  of  the  inner  hub  and  extending 
through  holes  in  the  outer  hub. 

The  so-called  triple  spoke  construction,  illustrated  in  Fig.  37S, 
is  generally  employed  for  automobile  wire  wheels.  One-half  of 
the  spokes  in  the  outer  row  extend  tangentially  in  one  direction 
and  the  other  half  in  the  opposite  direction.  The  inner  row  of 
spokes  and  the  intermediate  row  also  extend  in  opposite  direc- 
tions, respectively.  Owing  to  the  fact  that  the  thread  at  the 
outer  end  of  the  spokes  reduces  their  effective  cross  section  and 
that  that  portion  of  the  spoke  near  the  head  is  subjected  to  bend- 
ing stresses  in  addition  to  the  tension  on  it,  it  is  customary  to 
swage  down  the  middle  portion  of  the  spoke  so  as  to  make  it 
substantially  equal  in  strength  to  the  threaded  portion,  thus 
eliminating  unnecessary  weight.  In  order  to  secure  the  neces- 
sary lateral  strength  the  hubs  must  be  made  of  considerable 
length  and  the  spoke  flanges  placed  as  far  apart  as  possible. 

As  regards  the  necessary  size  of  spokes,  it  may  be  said  that  a 
touring  car  of  recent  design,  weighing  with  load  approximately 
5,000  pounds,  han,  36  inch  wire  wheels  with  56  spokes  each, 
swaged  down  at  their  middle  portion  to  ik  inch  diameter. 

Cast  Steel  Wheels — Probably  the  greatest  amount  of  trouble 
with  artillery  wood  wheels  has  been  experienced  with  those  used 
on  heavy  trucks.  Owing  to  the  very  thick  spokes  required  in 
these  wheels,  a  comparatively  slight  proportional  shrinkage  of 
the  spokes  causes  them  to  loosen  in  their  hubs,  and  the  rather 
severe  jarring  of  the  wheels  due  to  the  use  of  solid  tires  then 
has  a  very  destructive  action.  For  this  reason  cast  steel  wheels 
are  latterly  being  used  to  an  increased  extent  in  motor  truck 
practice.  These  wheels  were  first  used  in  Germany,  and  the 
greatest  amount  of  experience  with  them  has  been  gained  in  that 
country.  We  show  herewith  (Fig.  380)  a  sectional  view  of  the 
cast  steel  rear  wheel,  as  specified  for  German  military  trucks. 
These  trucks  are  designed  for  a  maximum  total  load  of  5^ 
metric  tons  on  the  rear  axle,  and  the  rear  driving  wheels  are  to 
be  fitted,  with  dual  solid  tires  of  41  inches  outside  diameter,  5.6 
inches  width  and  3.6  inches  depth,  the  cast  steel  portion  of  the 
wheel  being  34  inches  in  outside  diameter.  It  will  be  seen  that 
the  wheel  is  provided  with  a  hollow  spoke  of  about  3  inches 


ROAD  WHEELS. 


541 


FIG.  380.— CAST  STEEL  REAR  WHEEL  OF  GERMAN  MILITARY  TRUCK. 


542  ROAD  WHEELS. 

minimum  depth,  the  wall  of  the  spokes  as  well  as  the  inner 
wall  of  the  rim  being  a  shade  below  l/4  inch  in  thickness.  These 
wheels  are  provided  with  plain  parallel  bearings,  in  which  re- 
spect they  differ  from  cast  steel  wheels  used  in  this  coun- 
try, as  it  is  customary  here  to  use  anti- friction  bearings.  In 
the  majority  of  cases  the  spokes  are  made  cross  shaped,  which 
makes  the  molding  a  good  deal  easier,  but  the  hollow  round 
spoke  is  neater  in  appearance  and  also  has  the  advantage  with 
respect  to  lateral  strength,  at  least  in  the  case  of  trucks  of  large 
capacity. 

Floating  Bushings — Abroad  the  road  wheels  of  motor  trucks 
are  frequently  fitted  with  floating  bushings  instead  of  with 
antifriction  bearings  and  the  Government  specifications  for 
military  subsidy  vehicles  6f  some  countries  specify  these  bush- 
ings. One  of  the  advantages  of  this  construction  is  that  with 
it  the  wheel  can  be  quickly  removed  and  replaced  in  case  of 
tire  trouble.  Except  when  starting  from  rest,  a  plain  bearing 
with  floating  bushing  offers  not  very  much  more  resistance 
than  an  antifriction  bearing. 

In  order  to  ensure  satisfactory  lubrication,  the  clearance  on 
both  the  inside  and  outside  of  the  bushing  should  be  from 
0.008  to  0.012  inch,  for  diameters  of  3  to  4  inches.  If  the  clear- 
ance is  too  small  the  lubrication  is  not  so  dependable.  The 
bushings  are  drilled  with  numerous  oil  holes  and  it  is  recom- 
mended that  these  be  spaced  on  helical  lines.  The  bearing 
surfaces  of  both  the  axle  and  the  hub  must  be  carefully  ground 
and  polished,  and  unless  the  hub  is  of  a  metal  showing  a  fine 
texture,  it  is  best  to  bore  it  out  and  force  in  a  steel  liner  under 
hydraulic  pressure,  which  is  then  either  ground  or  reamed. 
The  wheel  bearings  should  be  so  proportioned  that  the  unit 
pressure  due  to  the  weight  and  traction  effort  combined,  does 
not  exceed  400  Ibs.  per  square  inch.  If  this  load  is  not  ex- 
ceeded and  if  the  lubricating  system  is  carefully  worked  out 
the  bushings  will  give  a  very  satisfactory  life. 


APPENDIX 


Clutch  Spring  Table. 

The  following  table  permits  of  readily  determining  the  size  of 
wire  required  for  clutch  springs  of  certain  lengths  and  diameters 
of  coil,  to  exert  a  certain  pressure.  D  denotes  the  mean  diam- 
eter of  the  coil  (from  centre  to  centre  of  wire),  which  is  equal 
to  the  outside  diameter  minus  the  diameter  of  the  wire;  d,  the 
diameter  of  the  wire;  IV,  the  maximum  safe  pressure  a  spring 
of  the  particular  diameter  of  coil  and  diameter  of  wire  will 
sustain,  and  F,  the  deflection  of  one  coil  under  a  pressure  of  100 
pounds.  It  will  be  noticed  that  three  different  values  are  given 
for  F  for  each  size  of  wire  and  diameter  of  coil ;  these  corre- 
spond to  coefficients  of  torsional  elasticity  of  10,000,000,  12,000,000 
and  14,000,000,  respectively.  The  maximum  safe  pressure  is  cal- 
culated on  the  basis  of  a  stress  of  50,000  pounds  per  square  inch. 


5/16' 


7/16" 


// 


D 

=   ll/2" 

\y&" 

154" 

l?/8" 

2" 

2/8" 

2  Y*" 

2H" 

W 

—  204.5 

188.5 

175.0 

163.4 

153.1 

144.1 

136.1 

129.0 

f.0697 

.0882 

.1108 

.1335 

.1643 

.1967 

.2390 

.2751 

F^  .0581 

.0735 

.0924 

.1109 

.1367 

.1639 

.1949 

.2293 

[.0498 

.0629 

.0791 

.0953 

.1172 

.1406 

.1671 

.1965 

W 

=  389.9 

367.3 

341.1 

318.3 

298.4 

280.9 

265.3 

251.3 

f.0283 

.0358 

.0450 

.0541 

.0667 

.0800 

.0951 

.1102 

F-!  .0236 

.0299 

.0375 

.0452 

.0555 

.0667 

.0793 

.0931 

1.0201 

.0256 

.0321 

.0387 

.0476 

.0571 

.0679 

.0799 

W 

=  663.1 

636.8 

591.3 

551.9 

517.4 

486.9 

459.9 

435.7 

f.0137 

.0174 

.0218 

.0263 

.0323 

.0388 

.0472 

.0542 

F\  .0114 

.0145 

.0182 

.0219 

.0269 

.0323 

.0384 

.0451 

[.0098 

.0124 

.0156 

.0188 

.0230 

.0277 

.0329 

.0387 

w 

=  1041. 

1009. 

936.9 

874.4 

819.8 

771.5 

728.7 

690.3 

f.0062 

.0079 

.0099 

.0119 

.0146 

.0176 

.0209 

.0246 

F]  .0052 

.0066 

.0082 

.0099 

.0122 

.0146 

.0174 

.0202 

[.0045 

.0056 

.0071 

.0085 

.0105 

.0126 

.0149 

.0175 

\v 

=  1636. 

1510. 

1402. 

1309. 

1227. 

1155. 

1091. 

1033. 

f.0044 

.0055 

.0069 

.0083 

.0102 

.0123 

.0146 

.0172 

F-i  .0036 

.0046 

.0058 

.0069 

.0084 

.0102 

.0122 

.0134 

[.0031 

.0041 

.0054 

.0060 

.0074 

.0089 

.0105 

.0124 

543 


544 


APPENDIX. 


APPENDIX. 


545 


J 
21 


.   ^ 


>   O    ON 
•VONO 


Tf   O   CO    VO    OO    »-i    CO 


t-Hrf     •         10 
O<X>-  O 

rxO-  o 


» 
OOOT-HrHi-H<M. 


rorJ-iot^OOONO^HCM- 
000000  -H.  rnr-i. 

t>»CJrOOOWl^W<NIO'« 

Tj-cocNimi^ON^Ococq' 
cvifO'd-io^ovo'^oocri- 
ooooooooo- 

t^OSCMOVOt^^OO 

OO^J-i-iOtXT-i^ClO 

T-lCMCOTfTfU-jlOlO 

C30C300C300 


C5000C3000 


OOOO^H^H 

.oooooo 


.      O  O  O  O 


PQPQPQPQPQPQ 


546 


APPENDIX. 


Ul 


CO 


!-4U  U 


il 


SH|T 


C/} 


•  H  \ 

i  » 

w  o  \ 


w  w  <^ 

?     w 


APPENDIX. 


547 


oc4iot^oui""jooiouio"">o«^o»ni/->o 

«••>  ^-  in  VO  00  O  O  ff)  CO  10  u->  OO  O  c«->  10  00  O  to  O 

vo  os  <N  m  oo  10  ^o  -H  .-i  rv  t^  r*5  o  \o  CM  oo  w>  t^  o 


r^Tj-O^OrOuimOOvotrirxOCMU'it^O 

CMOOTj-O\"">\OvOO\(^OOf-if«'5i-iCMr<5ir> 
COTt-^Ot^OCMCMu-ju-iONONCMUIC^CMmOO 
GOOOOi-i'-i'-i'-i'-'i-iCMCMCMf'SfSfi 


§ 

TJ-10 


"  t^  ^- O^O  fO  10  10  O  O  10  U";  t^  O  CM*^  t^  OLO  O 
roO\*r>OV£)t>.»^'-i'-i<NCMrciO\ot^OOOCNliO 


*+-    0\ 

O 


_  _  ,H  ,-<  ,-.  ,-<  C-q  CM  <N  CM  CM 


O^^oioiomcgcMCMCMCMCM 


i  CM  CM  CM  CM  CO 


I  I  I  I  I  I  I  I  I  I  I  I  I  I 

iAi^.ivi-vO-.^^CMCMfNCM 


548 


APPENDIX. 


d    <r>  >o  o>  4  N 


•*-   i* 

P      IX 


10  rx  M  tx  to  *^  tx  m  N  in  o  ^ 
tx  to  *o)  o  ON  oo  o  o\  oo  o*  tx  oo 


2 
£ 

"8 


£ 

I 


;mi 


s?  a  8    * 

1 


TJ-MOO     -*0     «     coiovooq     0_     roixO     Tttxw     tx«o 
fO^Ovooo^    ^     ^    J     ^    M-    ^     pj     fj    ro<nro44*^ 

-,?! 

cqco^-votxooov^^^^^^,,    „    „ 
o*oo«rtO»oo>oo«ooooooo 

tOtxON«OtxOMiOtxOiOOOOO 


IO  VO     Ix  OO     O     w 


W     tx    N     tx    tx  VO    vo 

i-i     N     ro^ftxO\N     ^•*> 


r  f  f  L  r  i  T  T  V  T  T  L  JLL  ^i  L  i      *, 


APPENDIX. 


54 


*^l/'o»oo 


H  to  ix 


II 
•r«    Q 


•B 

£ 


2  ^ 
&  & 


fJfOio\or>.oOOiHpjroiotN.OP|iotxO»'>O 

*«HMMI-<MM^NrJ^CO(OTf 

o    100    «r>ioinioioioioioio 
i?J^2^    ?^>5'hl   ^i   c?T?'t>9*c1    •^•*xc^^j-o\ 


O     N     10    tx    O     10    O 
10    »0     10    10 


uNCOT^iONOOOOOO*      *       *       *       *       * 


oo'^so    °    £oo>££.o    N"^ 

OOOO     txo'OOO     «     txo     >-<     IH 


£  S 
i  S" 


J.J. 


«    w    c<    o    w    eo 


li 

11 


550 


APPENDIX. 
S.  A.  E.  Six  Spline  Fittings. 


Permanent  fit. 


To  Slide  when  not         To  Slide  when  Under 
Under  Load.  Load. 


l^l^m 

r  —  - 

6—1 
w    = 
b    = 

a    = 

Nominal 

1 

.25  D 
.05  D 
,90  D 

w. 

1 

1 

T. 

^^m 

«  —  « 

6- 
w    = 
h    = 
a    = 

D. 

w^ 

t 

B, 

.25  D 
.0751 
.88  D 

a 

4 
> 

w. 

1 
1 

T. 

^^ 
-  a 

6- 
w    rr 
h    = 

a    = 

D 

w^ 

.  • 

-c. 

.251 
.101 
.801 

a 

1 
t 

> 

) 
) 

w. 

T 

.750 
44    .        .  .   

.675 

.188 

80 

,750 

.638 

.188 

117 

.750 

.600 

.188 

152 

.749 
.875 

.674 

.788 

.187 
.219 

109 

.749 

.875 

.637 
.744 

.187 
.219 

159 

.749 
.875 

.599 
.700 

.187 
.219 

207 

.874 
1.000 

| 

.787 
.900 

.218 
.250 

143 

.874 
1.000 

.743 
.850 

.218 
.250 

208 

.874 
1.000 

.699 
^800 

.218 
.250 

270 

.999 
1.125 

1.124 
1.250 

.899 
1.013 

1.012 
1.125 

.249 
.281 

.280 
.313 

180 
223 

.999 
1.125 

1.124 
1.250 

.849 
.956 

.955 
1.063 

.249 
.281 

.280 
.313 

263 
325 

.999 
1.125 

1.124 
1.250 

.799 
.900 

.899 
1.000 

.249 
.281 

.280 
.313 

342 
421 

1.249 
1.375 

1.124 
1.238 

.312 
.344 

269 

.1.249 
'1.375 

1.062 
1.169 

.312 
.344 

393 

1.249 
1.375 

.999 
1.100 

.312 
.344 

510 

1.374 
1.500 

1.237 
1.350 

.343 
.375 

321 

1.374 
1.500 

1.168 
1.275 

.343 
.375 

468 

1.374 
1.500 

1.099 
1.200 

.343 
.375 

608 

1.499 
1.625 

1.349 
1.463 

.374 
.406 

376 

1.499 
1.625 

1.274 
1.381 

.374 
.406 

550 

1.499 
1.625 

1.199 
1.300 

.374 
.406 

713 

1.624 
1.750 

1.462 
1.575 

.405 
.438 

436 

1.624 
1.750 

1.380 
1.488 

.405 
.438 

637 

1.624 
1.750 

1.299 

1.400 

.405 
.438 

827 

1749 
2.000 

o                           ._ 

1.998 
2.250 

1.574 
1.800 

1.798 
2.025 

.437 
.500 

.498 
.563 

570 
721 

1.749 
2.000 

1.998 
2.250 

1.487 
1.700 

1.698 
1.913 

.437 
.500 

.498 
.563 

823 

1,052 

1.749 
2.000 

1.998 
2.250 

1.399 
1.600 

1.598 
1.800 

.437 
.500 

.498 
.563 

1,080 
1,367 

2.248 
2.500 

2  028 
2.250 

.561 
.625 

891 

2.248 
2.500 

1.912- 
2.125 

.561 
.625 

1  300 

2.248 
2.500 

1.798 
2.000 

.561 
.625 

1  688 

2.498 
3.000 

O                                               „._,  

2.248 
2.700 

.623 
,760 

1,283 

2.498 
3.000 

2.123 
2.550 

.623 
.750 

1,873 

2.498 
3.000 

1.998 
2.400 

.623 
.750 

2,430 

2,998 

2.698 

.748 

2.998 

2.548 

.748 

2.998 

2.398 

.748 

T  =  1.000  X  6  X  mean  R  X  h  X  1  =  inch-pounds  torque  capacity  per  inch; 
bearing  length  at  1,000  Ibs.  pressure  per  square  inch  on  sides  of  splines.  No  allow- 
ance is  made  for  radii  on  corners  nor  for  clearances.  , 


APPENDIX. 
S.  A.  E.  Ten  Spline  Fittings. 


551 


Permanent  fit,. 


10— A 

w    =-  .156D 
h    =    .045  D 

a    =    .91  D 


To  Slide  when  not 
Under  Load. 


10— B. 

w    =    .156  D 
h    =    .07  D 
a    =    .8«D 


To  Slide  when  Undejf 
Load. 


10— C. 

w  —  .156  D 
h  =  .095  D 
a  =  .81 D 


Nominal 
diameter. 


1*4 


15* 


D. 

a. 

w. 

T. 

D. 

a. 

w. 

.750 

.683 

.117 

.750 

.645 

.117 

-  





120 

_ 

_____ 

- 

.749 

.682 

.116 

.749 

.644 

.116 

.875 

.796 

,137 

.875 

,753 

.137 





, 

165 

_ 

______ 

. 

.874 

.795 

.186 

.874 

.752 

.186 

1.000 

.910 

.156 

1.000 

.860 

.156 





215 





.999 

.909 

.155 

.999 

.859 

.155 

1.185 

1.024 

.176 

1.125 

.968 

.176 

1.124  1.023    .175 
1.250  1.138    .195 


1.249  1.137 
1.375  1.251 


.194 
.215 


1.374  1.250    .214 
1.500  1.365    .234 


1.499  1,364    .233 
1.625  1.479    .254 


1.624  1.478    .253 
1.750  1.593    .273 


1.749  1.592 
2.000  1.820 


.272 
.312 


1.998  1.818    .310 
2.250  2.048    .351 


2.248  2.046 
2.500  2.275 


.349 
.390 


2.498  2.273    .388 
3.000  2,730  -.468 


271 

336 

406 

483 

566 

658 

860 

1,088 

1,343 


2.998  2.728    .466 


1,934 


1.124     .967  .175 

1.250  1.075  .195 

1.249  1.074  .194 
1.375  1.183  .215 

1.374  1.182  .214 

1.500  1.290  .234 

1.499  1.289  .233 
1.625  1.398  .254 

1.624  1.397  .253 

l.,750  1.505  -.273 

1.749  1.504  .?72 

2.000  1.720  .312 

1.998  1.718  .310 

2.250  1.935  .351 

2.248  1.933  .349 

2.500  2.150  .390 

2.498  2.148  .388 

3.000  2.580  .468 

?.998  2.578  .466 


T. 
183 

248 
326 
412 
508 
614 
732 
860 


1,302 
1.647 
2,034 
2,929 


D. 

.750 

.749 
.875 

.874 
LOGO 


1.125 


a. 

.608 


w. 

.117 


.607    .116 
.709    .137 


.708    .136 
.810    .156 


.809   .155 
.911    .176 


1.124     .910  .175 

1.250  1.013  .195 

1.249  1.012  .194 

1.375  1.114  .215 

1.374  1.113  .214 

1.500  1.215  .284 

1.499  1  91  _  .238 

1625  1.316  .254 

1.624  1.315  .253 

1.750  1.418  .273 


997 


1.749  1.417 
2.0PO  1.620 


.272 
.312 


T. 
841 

839 

480 

545 

672 

813 

967 

1,185 

1,316 

1,720 

2,176 


1.998  1.618  .810 

2.250  1.823  .351 

2.248  1.821  .349 

2.500  2.025  .390 


2.498  2.023    .388 
3.000  2.430    .468 

< —  S.B69 

2,998  2.428   .466 


T  =  1,000  X  10  X  mean  R  X  h  X  1  =  inch-pounds  torque  capacity  per  inch; 
bearing  length  at  1,000  Ibs.  pressure  per  square  inch  on  sides  of  splines.  No  al- 
lowance is  made  for  radii  on  corners  nor  for  clearances. 


»52  APPENDIX. 

S.  A.  E.  Four  Spline  Fittings. 


Permanent  Fit 


w         /            H 

4-A 

w  equals  .241  D 
h  equals  .075  D 
d  equals    850  D 

\ 

4-B 

w  equals  .241  D 
h  equals  .125  D 
d  equals  .740  D 

m 

} 

Norn. 
Dia. 

D  ^ 

a 

w 

h 

T 

D 

a 

w 

h 

T 

M 

.750 

.637 

.181 

.056 

78 

.750 

.562 

.181 

.094 

123 

.749 

.636 

.180 

.055 

.749 

.561 

.180 

.093 

H 

.875 

.744 

.211 

.066 

107 

.875 

.656 

.211 

109 

167 

.8/4 

.743 

.210 

065 

.874 

.655 

.210 

108 

i 

1.000 

,850 

.241 

075 

139 

1.000 

.750 

.241 

.125 

219 

.999 

.849 

.240 

.074 

.999 

.749 

.240 

.124 

IX 

1.125 

.956 

.271 

084 

175 

1.125 

.844 

.271 

.141 

277 

1.124 

.955 

.270 

.083 

1.24 

.843 

.270 

.140 

IX 

1.250 

1.062 

.301 

.094 

217 

1.250 

.937 

.301 

.156 

341 

1.249 

1.061 

.300 

.093 

1.249 

.936 

.300 

.155 

i% 

1.375 

1.169 

.331 

.103 

262 

1.375 

1.031 

.331 

.172 

414 

1.374 

1.168 

.330 

.102 

1.374 

1.030 

.330 

171 

IX 

1.500 

1.275 

.361 

.112 

311 

1.500 

1.125 

.361 

.187 

491 

1.499 

1.274 

.360 

.111 

1.499 

1.124 

.360 

.186 

i% 

1.625 

1.381 

.391 

.122 

367 

11625 

1.219 

.391 

.203 

577 

1.624 

1.380 

.3^0 

.121 

1.624 

1.218 

.390 

.202 

W 

1.750 

1.487 

.422 

.131 

424 

1.750 

1.312 

.422 

.219- 

670 

1.749 

1.486 

.421 

.130 

1.749 

1.311 

.421 

.218 

2 

2.000 

1.700 

.482 

150 

555 

2.000 

1.500 

.482 

.250 

875 

1.998 

1.698 

.480 

.-148 

1.998 

1.498 

.480 

.248 

M 

2.250 

1.912 

.542 

.169 

703 

2.250 

1.687 

.542 

.281 

1106 

2.248 

1.910 

.540 

.167 

2.248 

1.685 

.540 

.279 

2H 

2.500 

2.125 

.602 

.187 

865 

2.500 

1.875 

.602 

.312 

1365 

2.498 

2.123 

.600 

.185 

2.498 

1.873 

.600 

.310 

3 

3.000 

2.550 

.723 

.225 

1249 

3.000 

2.250 

.723 

.375 

1969 

2.998 

2.548 

.721 

.223 

2.998 

2.248 

.721 

.373 

To  Slide  when  not  under 


T  equals  1000  x  4  x  Mean  R  x  h  x  1  equals  inch-pounds  torque  capacity  per  inch 
bearing  length  at  1000  Ibs.  pressure  per  square  inch  on  sides  of  splines.  No  allowance 
is  made  for  radii  on  corners  toor  for  clearance!. 


APPENDIX.  553 

S.  A.  C.  Standard  Lock  Washers. 

AUTOMOBILE    HEAVY    (FOR    GENERAL    USE). 

Bolt                                              Lock  Bolt                      Lock 

Diameter,                                 Washer  Section,  Diameter,  Washer  Section, 

Inches.                                           Inches.  Inches.                  Inches. 

3/16 1/16x1/16  11/16                      y4x*A 

y*  5/64x5/64      y*      V^A 

5/16 *AX#      %    17/64x17/64 

H  y&*y&      i     5/16x5/16 

7/16  11/64x11/64         1%        5/16x5/16 

ya  11/64x11/64  ij4  3/8xy8 

9/16  13/64x13/64  iti  ti*M 

Si    13/64x13/64  ll/3  7/16x7/16 

AUTOMOBILE    LIGHT    (FOR   OPTIONAL   USE   AGAINST    SOFT 
METAL). 

Bolt                                              Lock                             Bolt  /          Lock 

Diameter,                                Washer  Section,  Diameter,  Washer  Section, 

Inches.                                           Inches.                         Inches  Inches. 

3/16     1/16x3/64                       9/16  13/64x5/32 

Vt,     5/64x1/16                        ft  13/64x5/32 

5/16    Ys^/32                      11/16  ^x3/i6 

H    5*x-;/32  Y*  J*x3/i6 

7/16    H/64XJ6  H  17/64x3/16 

Y*     11/64x3*  i  5/I6XJ4 

The  outside  diameters  of  lock  washers  shall  coincide  prac- 
tically with  the  long  diameters  of  S.  A.  E.  standard  nuts,  which 
are  approximately  the  same  as  the  short  diameters  of  U.  S. 
standard  nuts.  The  inside  diameters  of  the  lock  washers  shall 
be  from  one-sixty-fourth  to  one-thirty-second  inch  larger  than 
the  bolt  diameters.  The  lock  washers  shall  be  parallel-faced  sec- 
tions, and  bulging  or  malformed  ends  must  be  avoided. 

Temper  Test. — After  compression  to  flat,  reaction  shall  be 
sufficient  to  indicate  necessary  spring  power,  and  on  a  subse- 
quent compression  to  flat,  the  lock  washer  shall  manifest  no 
appreciable  loss  in  reaction. 

Toughness  Test. — Forty-five  per  cent,  of  the  lock  washer,  in- 
cluding one  end,  shall  be  firmly  secured  in  a  vise,  and  45  per 
cent.,  including  the  other  end,  shall  be  secured  firmly  between 
parallel  jaws  of  a  wrench.  Movement  of  the  wrench  at  right 
angles  to  the  helical  curve  shall  twist  the  lock  washer  through 
45  degrees  without  sign  of  fracture,  and  movement  of  not  more 
than  135  degrees  shall  twist  the  lock  washer  entirely  apart. 


554 


APPENDIX. 


Light  Series  of  Radial  Ball  Bearings. 


Corner 

Radial 

No.  of 

at  Bore  of 

Load 

Bear- 

— Bore.  — 

Diameter. 

—  Width.  —         Inner  Race. 

in 

ing. 

Mm. 

Inches. 

Mm. 

Inches. 

Mm.     Inches.      Mm.    Inches. 

Lbs. 

200 

10 

•39370 

30 

i  .18110 

9       0.35433 

0.04 

120 

201 

12 

.47244 

32 

1.25984 

10       0.39370 

0.04 

140 

202 

IS 

.59055 

35 

1-37795 

ii       0.43307 

0.04 

160 

203 

17 

.66929 

40 

1.57481 

12       0.47244 

0.04 

250 

204 

20 

.78740 

47 

1.85040 

14       0.55118 

0.04 

320 

205 

25 

.98425 

52 

2.04725 

15       0.59055 

0.04 

350 

206 

30 

.  18110 

62 

2.44095 

i  6       0.62992 

0.04 

550 

207 

35 

•37795 

72 

2.83465 

17       0.66929 

0.04 

600 

208 

40 

.57481 

80 

3-14962 

i  8       0.70866 

0.08 

860 

2O9 

45 

.77166 

85 

3.34647 

19       0.74803 

0.08 

9S« 

2IO 

50 

.96851 

90 

3.54332 

20          0.78740 

0.08 

IOOO 

211 

55 

.16536 

IOO 

3.93702 

21           0.82677 

0.08 

1  1  60 

212 

60 

.36221 

no 

4.33072 

22          0.86614 

0.08 

1550 

213 

65 

.55906 

120 

4.72443 

23          0.90551 

0.08 

1670 

214 

70 

2.75591 

125 

4.92128 

24          0.94488 

0.08 

1820 

215 

75 

2.95277 

130 

5.11813 

25          0.98425 

0.08 

2130 

216 

80 

3.14962 

140 

5-51183 

26 

[.02362         3         0.12 

2650 

217 

85 

3.34647 

150 

5.90554 

28 

[.10236         3         0.12 

2850 

218 

90 

3-54332 

1  60 

6.29924 

30 

[  .  18110         3          o.  12 

3400 

2IQ 

95 

3.74017 

170 

6.69294 

32 

1.25984         3         0.12 

3750 

220 

100 

3.93702 

180 

7.08664 

34 

1.33858          3          0.12 

3950 

221 

105 

4.13387 

190 

7-48035 

36 

1.41732          3          0.12 

4600 

222 

no 

4.33072 

200 

7.87405 

38 

1.49607         3         0.12 

5000 

Heavy  Series  of  Radial 

Ball  Bearings. 

Corner 

Radial 

No.  of 

at  Bore  of 

Load 

Bear- 

— Bore.— 

Diameter. 

—Width.—         Inner  Race. 

in 

ing. 

Mm. 

Inches. 

Mm. 

Inches. 

Mm. 

Inches.      Mm.    Inches. 

Lbs. 

403 

17 

.66929 

62 

2.44095 

17 

.66929         i 

0.04 

850 

404 

20 

.78740 

72 

2.83465 

IQ 

.74803         2         0.08 

1050 

405 

25 

.98425 

80 

3-14962 

2  I 

.82677         2         0.08 

1320 

406 

30 

.18110 

90 

3-54332 

23 

.90551         2         0.08 

1600 

407 

35 

•37799 

IOO 

3.93702 

25 

.98425             2             0.08 

1900 

408 

40 

.5748i 

no 

4-33072 

27 

.06299             2             O.O8 

220O 

409 

45 

.77166 

120 

4.72443 

29 

.14173             2             0.08 

2500 

410 

50 

.96851 

130 

5-11813 

31 

.22047             2             O.O8 

3400 

411 

55 

.16536 

140 

5.5"83 

33 

.29921          3          o.i  2 

3900 

412 

60 

.36221 

150 

5.90554 

35 

•37795         3         0.12 

4400 

413 

65 

.55906 

1  60 

6.29924 

37 

.45669         3         0.12 

4900 

414 

70 

•75591 

180 

7.08664 

42 

•65355         3         0.12 

62OO 

4»S 

75 

•95277 

190 

7.48035 

45 

.77166         3         0.12 

6600 

416 

80 

3-14962 

200 

7.87405 

48 

.88977          3          0.12 

7300 

4*7 

85 

3.34647 

210 

8.26775 

52 

.04725          3          0.12 

8580 

418 

90 

3.54332 

225 

8.85830 

54 

.12599         3          0.12 

IOOOO 

419 

95 

3.74017 

250 

9-84256 

55       2.16536          3          0.12 

11880 

420 

100 

3.93702 

265 

10.43311 

60       2.36221         3         0.12 

14,000 

APPENDIX. 
Medium  Series  of  Radial  Ball  Bearings. 


555 


Corner 
Mo.  of                                                                                             at  Bore  of 
Bear-      —  Bore.  —              Diamettr.            —  Width.  —         Inner  Race, 
ing.     Mm.     Inches.      Mm.     Inches.      Mm      Inches.      Mm.    Inches. 

Radial 
Load 

in 
Tbs. 

300       10 

0-39370       35        J-37795        "        0.43307 

I 

0.04 

200 

301        12 

0.47244       37       1.45669       12       0.47244 

I 

0.04 

240 

302       15 

0.59055       42       1.65355        13       0.51181 

I 

0.04 

280 

303       17 

0.66929       47        1.85040        14       0.55118 

I 

0.04 

370 

304          20 

0.78740        52       2.04725        15       0.59055 

I 

0.04 

440 

305          25 

0.98425       62       2.44095        17       0.66929 

I 

0.04 

620 

306         30 

i.  18110       72       2.83465        19       0.74803 

2 

0.08 

860 

307       35 

1-37795       80       3.14962       21        0.82677 

2 

0.08 

I  100 

308       40 

1.57481        90       3-54332       23        0.90551 

2 

0.08 

MS0 

309       45 

1.77166     100       3-93702       25       0.98425 

2 

0.08 

1750 

310       50 

1.96851      no       4.33072       27        1.06299 

2 

0.08 

2IOO 

3"       55 

2.16536     120       4.72443       29        1.14173 

2 

0.08 

2400 

312       60 

2.36221      130       5.11813       31        1.22047 

2 

0.08 

2800 

313       65 

2.55906     140       5.51183       33        1.29921 

3 

O.  12 

3300 

3*4       7° 

2.75591      150       5-90554       35        1-37795 

3 

O.  12 

4000 

315       75 

2.95277     160       6.29924       37        1.45669 

3 

0.12 

4400 

316       80 

3.14962     170       6.69294       39     .1.53544 

3 

O.  12 

5OOO 

317       85 

3.34647     180       7.08664       41        1.61418 

3 

O.  12 

5700 

318       90 

3-54332     190       7-48035       43        1.69292 

3 

0.12 

6400 

3i9       95 

3.74017     200       7.87405       45        1.77166 

3 

O.  12 

70OO 

32O       TOO 

3.93702     215       8.46460       47        1.85040 

3 

O.  12 

7700 

321        105 

4.13387     225       8.85830       49        1.92914 

3 

0.  12 

8400 

322     no 

4.33072     240       9.44886        50        1.96851 

3 

0.  12 

IOOOO 

S.  A. 

C.  Tolerances  for  Radial  Ball  Bearings. 

f\  .1       r»_        ™  T>  

W'Hth 

Plus      Minus    Total       Plus     Minus     Total 

Plus 

Minus 

Total 

Bearing 

Lim-       Lim-      Lim-       Lim-       Lim-       Lim- 

Lim- 

Lim- 

Lim- 

Numbers. 

its,         its.         its.           its.          its.          its. 

its. 

its. 

its. 

200  to  204 

o       .0006     .0006       .0002     .0004     .0006 

0 

.002 

.002 

300  to  303 

o       .0006     .0006       .0002     .0004     .coo6 

0 

.002 

.002 

205  to  215 

o       .0008     .0008       .0002     .0004     .0006 

o 

.OO2 

.002 

304  to  316 

0          .0008       .0008          .0002       .0004       .0006 

0 

.002 

.002 

403  to  411 

o       .0008     .0008       .0002     .0004     .0006 

o 

.OO2 

.OO2 

217  tO  222 

O          .OOI2       .0012          .OOO2       .COO4       .OOO6 

o 

.002 

.002 

3I4t03I9 

o       .0012     .0012       .0002     .0004     .0006 

C 

.002 

.002 

412  to  416 

0          .0012       .0012          .0002       .0004       .OOO6 

0 

.OO2 

.002 

556 


APPENDIX. 


(A 

bo 


1 


UJ 

< 

CO 


II 


8888  8888   8888   888 


<O«DCO«O     oooooooo     oooooo 


)OOO      OOOO 


!888   8888   8888   888 


§888   888 

oooo  oooo  oooc?  oooo  ooo 

s 


APPENDIX 


557 


| 


I 


U4 


CO 


Ill 


il 


OOOOOOOO      « 

8888   8888   8 


888   8888   8888   8 


•^TfOOOO       OOOOOOOO       00(N(N(N       M  (N  N  C^       *3 

pppp     pppp     P*-"-;^     '-H'-JI-J^      »-j 

eo 


OOOOO       OOOOOOOO       OOOOC^C^l       WNNd       N 

oooo  oooo  oooo  oooo  o 


S8   882 


O^?O*O      »-<«Oi-i«O      »H«pi-(l 
•>t<N>-<a>       00  «D  10  CO       <NOO5I 


ICIO          T}<^Tf<-^          CO 

t>  o>     i-Hco»ot^     O; 
eocococo     eo 

8 


22   2222 


558 


APPENDIX. 


S.  A.  C.  Standard  Wheel   Dimensions  for  Solid 

Tires. 

DEMOUNTABLE    AND   NON-DEMOUNTABLE    RIMS. 

Single  Tires. 

Width  of  felloe  and  band,  M  inch  less  than  sectional  size  of  tire.  Thickness 
of  steel  band,  J4  inch  up  to  4J4  inch  tire;  ^  inch  on  4^  inch  and  larger 
tires. 

Dual  Tires. 

Width  of  felloe  and  band,  twice  the  sectional  size  of  tire.  Thickness  of 
steel  band,  ^  inch  for  all  sizes  of  tire. 

Single  and  Dual  Tires. 

Inches.  Inches.  Inches.  Inches.  Inches. 
Sectional  size  of  tire  .............   2             2*6         3  3^         4 

Minimum    felloe    thickness  ........    iJ4         ilA         i/4         iJA         i$4 

Sectional  size  of  tire  .............  4*A         S  S*A         6         6l/2  and  over 

Minimum    felloe    thickness  ........    i$4         2  2  2  2% 


WHEEL    DIAMETER    OVER    STEEL   BAND. 
Single  and  Dual  Tires. 


Inches, 
36 
30 


Inches.       Inches.          Inches. 

Nominal  outer  diam.  of  tires. ...   30  32  34 

Wheel  diam.  over  steel  band....   24  26  28 

Exact    circumference    over    steel 

band;  neglecting  tolerance 7525/64     8111/16     8731/32  94^ 

Inches.  Inches.  Inches. 

Nominal  outer  diam.  of  tires. ...   38  40  42 

Wheel  diam.  over  steel  band. ...   32  34  36 

Exact    circumference    over    steel 

band;  neglecting  tolerance 10017/32  10613/16  "33/32 

Allowable  Deviation  from  Precision  in  Felloe  Bands. 

Plus  Minus 

Inches.  Inches. 

Tolerance  in  circumference  of  band  before   application..    1/32  1/32 

Tolerance  in  circumference  of  band  after  application 1/16  1/32 

Tolerance  of  thickness   of   band 0.006  0.006 

Tolerance  in  radius  of  band  after  application 1/16  1/16 

Tolerance  in  width   of   felloe   band — 

Up  to  and  including  4  inches 1/32  1/32 

4  1/16  to  6  inches 3/64  3/64 

6  1/16  to  12  inches 1/16  1/16 

Variation  in  trueness  of  band  when  placed  on  surface  plate — 

Band  shall  touch  at  all  points  within   1/32  inch  up  to  and  including  6 
inch  width.     Over  6  inch  width  within  1/16  inch. 

MEASURING  CIRCUMFERENCE  OF  BAND. 

In  measuring  circumference  of  band,  if  there  is  not  an  allow- 
ance on  the  tapeline  itself,  a  correction  amounting  to  three  times 
the  thickness  of  the  tapeline  should  be  made. 

NOTE.— All  of  the  foregoing  summary,  so  far  as  pertinent,  ap- 
plies to  metal  wheels. 


APPENDIX. 


559 


BOLT  EQUIPMENT  FOR  SIDE  FLANGES. 

All  Bolts  to  Be  y2   Inch  Diameter. 

Outside  Diameter 

Outside  Diameter 

Bolt  Diameter 

Number                Bolt  Diameter 

Number 

Tire  Hole  Circle. 

of  Bolts.             Tire  Hole  Circle. 

of  Bolts. 

26  isy2 

6,   9   or   18             42  34}4 

10,   15   or  30 

28  20y2 

do.                    44  36^ 

12,   18   or  36 

30  22^ 

do.                    46  3Sy2 

do. 

32  24*/2 

8,   12  or  24           48  40}4 

do. 

34  26y2 

do.                    50  42}4 

14,  21   or  42 

36  28y2 

do.                    52  44y2 

do. 

38  30J4 

10,   15   or  30           54  46}4 

do. 

40  32H 

do. 

• 

Dimensions  of  Wrought  Iron  Pipes. 

Nominal 

Actual  Inside       Actual  Outside 

No. 

Diameter, 

Diameter,               Diameter, 

of  Threads 

Inches. 

Inches.                   Inches. 

Per  Inch. 

% 

,  0.27                         0.405 

27 

1A 

0.364                       0.54 

18 

H    

0.494                       0.675 

18 

j4    

0.623                       0.84 

14 

54    

0.824                       1.05 

14 

1 

1.048                       1.315 

\\y2 

154    

1.38                         1.66 

ny2 

154    

1.61                         1.90 

iiX 

2       

1.067                       2.375 

ny> 

2J4 

2.468                       2.875 

8 

3       

3.067                       3.5 

8 

560 


APPENDIX. 
S.  A.  £•  Steel  Specifications. 


Spec. 

No. 

C. 

Mn. 

P.* 

S.* 

Ni. 

Cr. 

V.** 

CARBON 

STEELS. 

1010 

.05-.15 

.30-.60 

.045 

.05 

1020 

.15-.25 

.30-.60 

.045 

.05 

1025 

.20-.30 

.50-.80 

.045 

.05 

1035 

.30-.40 

.SO-.80 

.045 

.05 

1045 

.40-.SO 

.50-.80 

.045 

.05 

1095 

.90-1.05 

.25-.50 

.04 

.05 

1114J 

.08-.20 

.30-.80 

.12 

.06-.12 

NICKEL 

STEELS. 

2315 

.10-.20 

.50-.80 

.04 

.05 

3.25-3.75 

2320 

.15-.25 

.50-.80 

.04 

.045 

3.25-3.75 

2330 

.2S-.35 

.50-.80 

.04 

.045 

3.25-3.75 

2335 

.30-.40 

.50-.80 

.04 

.045 

3.25-3.75 

2340 

.35-.4S 

.50-.  80 

.04 

.045 

3.25-3.75 

2345 

.40-.50 

.50-.80 

.04 

.045 

3.25-3.75 

3120 

.15-.25 

.50-.  80 

.04 

.045 

.00-1.50 

.45-.7S 

3125 

.20-.  30 

.50-.80 

.04 

.045 

.00-1.50 

.4S-.75 

3130 

.25-.3S 

.50-.80 

.04 

.045 

.00-1.50 

.45-.7S 

3135 

.30-.40 

.50-.  80 

.04 

.045 

.00-1.50 

.4S-.75 

3140 

.35-.4S 

.50-.80 

.04 

.045 

.00-1.50 

.4S-.75 

3220 

.15-.25 

.30-.  60 

.04 

.04 

.50-2.00 

.90-1.25 

3230 

.25-.3S 

.30-.60 

.04 

.04 

.50-2.00 

.90-1.25 

3240 

.3S-.45 

.30-.60 

.04 

.04 

.50-2.00 

.90-1.25 

3250 

.45-.  55 

.30-.60 

.04 

.04 

.50-2.00 

.90-1.25 

X3315 

.10-.20 

.45-.7S 

.04 

.04 

2.75-3.25 

.60-.95 

X3335 

.30-.40 

.45-.7S 

04 

.04 

2.75-3.25 

.60-.95 

X3350 

.4S-.55 

.45-.7S 

.04 

.04 

2.75-3.25 

.60-.95 

3320 

.15-.25 

.30-.60 

.04 

.04 

3.25-3.75 

1.25-1.75 

3330 

.2S-.35 

.30-.60 

.04 

.04 

3.25-3.75 

1.25-1.75 

3340 

.3S-.45 

.30-.60 

.04 

.04 

3.25-3.75 

1.25-1.75 

CHROME  NICKEL  STEELS. 

5120 

.15-.25 

t 

.04 

.045 

.65-.8S 

5140 

.35-.4S 

t 

.04 

.045 

.6S-.85 

5165 

.60-.  70 

t 

.04 

.045 

.65-.8S 

5195 

.90-1.05 

.20-.45 

.03 

.03 

.90-  .10 

51120 

1.10-1.30 

.20-.  45 

.03 

.03 

.90-  .10 

5295 

.90-1.05 

20-.  45 

.03 

.03 

1.10-  .30 

52120 

1.10-1.30 

.20-.45 

.03 

.03 

1.10-  .30 

VANADIUM  STEELS. 

6120 

.15-.25 

.50-.80 

.04 

.04 

.80-  .10 

.15 

6125 

.20-.30 

.50-.  80 

.04 

.04 

.80-  .10 

.15 

6130 

.25-.3S 

.50-.80 

.04 

.04 

.80-  .10 

.15 

6135 

.30-.  40 

.50-.  80 

.04 

.04 

.80-  .10 

.15 

6140 

.3S-.45 

.50-.80 

.04 

.04 

.80-  .10 

5 

6145 

.40-.  50 

.50-.  80 

.04 

.04 

.80-  .10 

.15 

6150 

.45-.S5 

.50-.  80 

.04 

.04 

.80-  .10 

.15 

6195 

.90-1.05 

.20-.45 

.03 

.03 

.80-  .10 

.15 

SILICO-MANCANESE  STEELS. 

9250 

.45-.S5 

.60-.80 

.045 

.045 

1.80-2.10% 

Si 

9260 

.5S-.65 

.50-.70 

.045 

.045 

1.50-1.80%  Si 

*  Not  to  exceed.  fTwo  types  of  steel  are  available  in  this  class,  viz.,  one 
with  manganese  .25-. 50  per  cent,  and  silicon  not  over  .20  per  cent.  ;  the 
other  with  manganese  .60-. 80  per  cent,  and  silicon  .15-. 50  per  cent.  **Not 
less  than.  |Screw  stock;  the  amount  of  sulphur  in  this  case  is  to  be  between 
the  limits  given. 


APPENDIX  561 

List  of  Heat  Treatments. 

A  —  After  forging  or  machining  carbonize  at  between  1600°  and  1750°  F. 
(1650-1700°  F.  desired),  cool  slowly  or  quench,  reheat  to  1450°-1500°  F. 
and  quench. 

B  —  After  forging  or  machining  carbonize  at  between  1600°  and  1750°  F. 
(16SO°-1700°  desired),  cool  slowly  in  the  carbonizing  mixture,  reheat  to 
1550°-1625°  F.,  quench,  reheat  to  1400°-1450°  F.,  quench,  draw  in  hot  oil  at 
from  300°  to  450°  F.,  depending  upon  the  hardness  desired. 

D  —  After  forging  or  machining  heat  to  1500°-1600°  F.,  quench,  reheat  to 
1450°-!  500°  F.,  quench,  reheat  to  600M2000  F.  and  cool  slowly. 

E—  After  forging  or  machining  heat  to  1500°-!  550°  F.,  cool  slowly,  reheat 
to  14SO°-1500°  F.,  quench,  reheat  to  600°-1200°  F.  and  cool  slowly. 

F  —  After  shaping  or  coiling  heat  to  1425°-1475°  F.,  quench  in  oil,  reheat 
to  400°-900°  F.,  in  accordance  with  degree  of  temper  desired  and  cool 
slowly. 

G—  Carbonize  at  between  1600°  and  1750°  F.  (1650°-1700°  F.  desired), 
cool  slowly  in  the  carbonizing  material,  reheat  to  1500°-!  550°  F.,  quench, 
reheat  to  1300°-1400°  F.,  quench,  reheat  to  250°-500°  F.  (in  accordance 
with  the  necessities  of  the  case)  and  cool  slowly. 

H  —  After  forging  or  machining  heat  to  1500°-1600°  F.,  quench,  reheat  to 
600°-1200°  F.  and  cool  slowly. 

K  —  After  forging  or  machining  heat  to  1500°-1550°  F.,  quench,  reheat 
to  1300°-1400°  F.,  quench,  reheat  to  600°-1200°  F.  and  cool  slowly. 

L  —  After  forging  or  machining  carbonizing  at  a  temperature  between 
1600°  and  1750°  F.  (1650°-1700°  desired),  cool  slowly  in  the  carbonizing 
mixture,  reheat  to  1400°-1SOO°  F.,  quench,  reheat  to  1300°-1400°  F.,  quench, 
reheat  to  250°-500°  F.  and  cool  slowly. 

M  —  After  forging  or  machining  heat  to  1450°-!  500°  F.,  quench,  reheat  to 
500°-1250°  F.  and  cool  slowly. 

P  —  After  forging  or  machining  heat  to  1450°-!  500°  F.,  quench,  reheat  to 
1375°-1450°  F.,  quench,  reheat  to  500°-12SO°  F.  and  cool  slowly. 

Q  —  After  forging  heat  to  147S°-1525°  F.,  hold  at  this  temperature  one-half 
hour  to  insure  thorough  heating,  cool  slowly,  reheat  to  1375°-1425°  F., 
quench,  reheat  to  250°-550°  F.  and  cool  slowly. 

R—  After  forging  heat  to  1500°-1550°  F.,  quench  in  oil,  reheat  to  1200°- 
1300°  F.,  hold  at  this  temperature  three  hours,  cool  slowly,  machine  heat 
to  13SO°-14SO°  F.,  quench  in  oil,  reheat  to  2SO°-SOO°  F.  and  cool  slowly. 

S  —  After  forging  or  macJiining  carbonize  at  a  temperature  between 
1600°  and  1750°  F.  (1650°-1700°  F.  desired),  cool  slowly  in  the  carbonizing 
mixture,  reheat  to  16SO°-1750°  F.,  quench,  reheat  to  1475°-1SSO°  F..  quench, 
reheat  to  250°-550°  F.  and  cool  slowly. 

T  —  After  forging  or  machining  heat  to  16SO°-1750°  F.,  quench,  reheat  to 
500°-1300°  F.  and  cool  slowly. 

U  —  'After  forging  heat  to  1525°1600°  F.,  hold  at  this  temperature  for  half 
an  hour,  cool  slowly,  reheat  to  1650°-1700°  F.,  quench,  reheat  to  350°-5SO° 
F.  and  cool  slowly. 

V  —  After  forging  or  machining  heat  to  1650°-!  750°  F.,  quench,  reheat  to 
400°-  1200°  F.  and  cool  slowly. 

Heat  Treatments  For  Different  Steels. 

SPECIF.  No.  HEAT  TREATMENTS.  SPECIF.  No.         HEAT  TREATMENTS 

1020  A,  B  and  H  X  3335  P  and  R 

1025  B  and  H  X  3350  P  and  R 

1035  D,  E  and  H  3320  L 

E  and  H  3330  P  and  R 

1095  F  3340  P  and  R 

2315  G  5120  B 

2320  G,  H  and  K  5140  H  and  D 

J330  H  and  K  5195  P  and  R 

2335  H  and  K  51120  P  and  R 

2340  H  and  K  5295  P  and  R 

120  G,  H  and  D  52120  P  and  R 

3125  H,  D  and  E  6120  S   and  T 

3130  H,  D  and  E  6125  T 

3135  H,  D  and  E  6130  T 

T 


3140         H,  D  and  E  6135 

3220         G,  H  and  K  6140        T 

H  and  D  6145         T  and  U 

3240         H  and  D  6150 

3250         M  and  Q  9250 
X  3315         G  and 


u                                 01^5  i 

D                               6150  U 

S9250  V 

9260  V 


562  APPENDIX 

1917  American  Truck  Practice. 


*  CYLINDER   GROUPING. 

Cast  En  Bloc 61  % 

Cast  in  Pairs 36.5  % 

Cast    Singly    2.5  % 

CYLINDER  TYPES. 

L-Head    83      % 

T-Head 12.25% 

Valve   in   Head 4      % 

FUEL  FEED. 

Gravity   Feed    82.2  % 

Vacuum   Feed    13.5   % 

Pressure  Feed   4.3  % 


IGNITION. 

Magneto    95 

Battery    5 

Single   System    76 

Double  Systems    24 

COOLING  WATER  CIRCULATION. 

By    Pump    79.6 

By  Thermo-Syphon    20.4 

CLUTCH  TYPES. 

Cone    25 

Dry  Disc    64 

Lubricated    Disc    .  11 


NUMBER  OF   FORWARD  SPEEDS. 

Three-Speed     79      % 

Four-Speed     21      % 


TRANSMISSION  LOCATION. 

On  Engine   52  % 

'Midships     47.3  % 

On  Axle    0.7  % 

AXLE  TYPES. 

Dead   Axles 31  % 

Live    Axles    69  % 

TYPES  OF  LIVE  AXLES. 

Full   Floating 59  % 

Three-quarter    Floating 7  % 

Semi-Floating     34  % 

FRAMTS. 

Pressed    Steel    68  % 

Rolled    Section     Steel 32  % 

STEERING  GEAR   LOCATION. 

Left  Hand    Side 71  % 

Right   Hand   Side 29  % 


REPRESENTATIVE  TIRE  EQUIPMENT. 


Capacity. 

1  Ton 
ll/2  Tons 

2  Tons 
2]/2  Tons 

3  Tons 
3l/2  Tons 

4  Tons 

5  Tons 
7  Tons 


Front 


36  x  4 


x  4 
x  5 


36  x  5 
36  x  5 
36  x  6 
36  x  6 


Rear 
34  x  4 
36  x  5 
36  x  6 
36  x  4d 
36  x  5d 
36  x  5d 
36  x  5d 
36  x  6d 
40  x  7d 


American  Pleasure  Car  Practice. 


CLUTCH  TYPES. 

1917       1915  1913 

Cone    34    %     50    %  54.2% 

Disc    66    %     46.2%  42.2% 

Others    3.8%  3.6% 

NUMBER  OF  SPEEDS  FORWARD. 

Two    0.7%       3.8%        

Three 89.5%     69.5%  69.2% 

Four    9.8%     26.7%  30.8% 

GEAR  Box  LOCATION. 

On    Engine... 75     %     49.7%  40.4% 

Amidships  ...14.6%     32.7%  44.6% 

On  Rear  Axle.  10.4%     17.6%  15.0% 

FINAL  DRIVE. 

Bevel   Gear... 29.3%     81.9%        

Helical    Bevel 

Gear    68.0%     12.5% 

Chain   2.0%       2.5% 

Worm    1.9%        

Special    0.7%       1.2%        


REAR  SPRINGS. 

1917 

1915 

1913 

Half    Elliptic.  29.4% 

15.2% 

10.6% 

Three-quarter 

Elliptic     ...28.7% 

58.2% 

69.0% 

Elliptic     6.3% 

9.3% 

9.6% 

Platform    ....    3.5% 

6.0% 

8.4% 

Cantilever     .  .29.4% 

9.3% 

Special     - 





REAR  AXLES. 

Semi-Floating.27.1% 

20.9% 

21.0% 

Three   quarter 

Floating    ..24.5% 
Seven  eighths 

26.8% 

10.0% 

Floating  ..  .    1.4% 





Full  Floating.  45.0% 

52.3% 

69.0% 

Dead    2.0% 





INDEX. 


PAGE. 

Accelerator    Pedals 450 

Alco   Drop   Forged  Axle 246 

Axle    Housings 233 

Axle  Tube  Bending  Moments 239 

Axle     Tubes 234 

Axle  Tubes,  Methods  of  Fitting 235 

Axle  Tubes,  Stresses  in 237 

Axle  Weight   Formula 214 

Axles,    Dead 9 

Axles,    Live 9 

Ball  Mounted  Control  Lever 465 

Band  Clutch 53 

Band  Clutch,  Sample  Calculation  of 59 

Band  Clutch,  Effect  of  Centrifugal   Force  on 60 

Band  Clutch,  Theory  of 56 

Bevel  Gear  Bearing  Loads 93 

Bevel  Gear  Blanks,  Calculation  of 219 

Bevel  Gear  Efficiency 278 

Bevel     Gear     Helical 215 

Bevel  Gear  Pinion  Bearings,   Mounting  of 250 

Bevel  Gears,  Straight 232 

Bevel  Gears,  Grinding  in 290 

Bevel   Gears,   Strength  of 222 

Bevel  Gears,  Manufacture  of  Helical 231 

Bevel  Gears,  Thrust  Loads  on  Helical 224 

Bevel  Pinion  Blanks,  Turning  up 291 

Bevel   Spur  Drive 341 

Bowden  Wire  Mechanism 446 

Brake     Adjustment 377 

Brake  Dimensions,  Determination  of 363 

Brake    Drums 363 

Brake  Drums,   Securing 534 

Brake    Equalizers 378 

Brake   Expanding  Mechanism 372 

Brake  Facing  Materials 375 

Brake   Members,    Stresses   in 369 

Brake    Releasing    Means 366 

Brake  Rod  Adjustment 479 

Brake  Rod,  Adjustment  of 380 

Brake  Shoes,  Air  Cooled 367 

Brakes,   Calculation  of   Band 369 

Brakes,    Contracting 354 

Brakes,  Details  of   Expanding 375 

Brakes,  Front  Wheel 333 

563 


564  INDEX. 

PACK. 

Brakes,  Location  of 358 

Brakes,  Number  of 357 

Brakes,  Service  and  Emergency 360 

Brakes    and     Skidding 383 

Brakes,  Types  of 357 

Braking  Power,  Calculation  of 360 

Chain  Adjusting  Rods 329 

Chain  and  Sprocket  Calculations 325 

Chain  Cases 336 

Chain  Drive 323 

Chain  Pull 327 

Chain,  Construction  of 323 

Chamfering    Sliding    Gears 109 

Change  Gear  Bearing  Mounting 112 

Change    Gear    Bearing    Pressure 82 

Change  Gear  Bearing  Sizes 96 

Change  Gear  Calculation  Example 80 

Change  Gear  Intermediate  Bearings 98 

Change   Gear   Layouts 76 

Change    Gear    Shaft    Dimensions 99 

Change  Gear,  History  of 69 

Change  Gear,  Positive  Clutch  Type 120 

Change   Gear,   Running   in   of 119 

Change  Gear,   Silent  Chain  Type 122 

Change  Gears,  Allowable   Stress  in 78 

Change  Gears,  Manufacture  of 107 

Change  Speed  Gear,  Purpose  of 7 

Clutch  and  Brake,   Interconnection  of 457 

Clutch   Brakes 30 

Clutch  Connection  to  Change  Gear 66 

Clutch     Disc     Lubrication 48 

Clutch    End    Thrust 68 

Clutch    Shaft    Dimensions 65 

Clutch  Shifting  Collar   28 

Clutch  Spring  Inside  Shaft 47 

Clutch  Springs • 27 

Clutches,  Classification  of 12 

Cone,  Angle  of 14 

Cone  Clutch  Calculation 14 

Cone  Clutch  Calculation  Chart 19 

Cone    Clutch    Centre 24 

Cone  Clutch  Engagement  Springs 22 

Cone  Clutch,  Constructional  Details  of 20 

Cone  Clutch,  Leather,  Pattern  for 2J 

Cone  Clutch  Thrust  Bearing 25 

Cone   Clutch,   Multiple   Spring  Type 23 

Cone  Clutch,  Pressed   Steel 27 

Cone  Clutch  Types 13 

Cone  Clutches,  Unit  Normal  Pressure  in 16 

Cone  Diameter 16 

Control,  Centre 460-465 

Control  Joints 449 

Control,   Left    Hand 460 


INDEX.  565 

PAGE. 

Control  Lever  on  Steering  Post 447 

Control  Levers 461 

Control   Ratchet 441 

Control,  Single  Pedal 458 

Control,  Selective 464 

Control,  Spark  and  Throttle 441 

Critical  Speeds  of  Shafts 279 

Daimler  Worm  Driven  Axle 320 

Differential    Bearings 256 

Differential  Gear,  Action  of 180 

Differential    Gear,    Calculation   of    Bevel   Type 181 

Differential  Gear,  M.   &  S.   Helical 190 

Differential,    Gearless    Type 191 

Differential    Gear,    Spur    Type 187 

Differential   Gear,  Purpose  of 6 

Differential  Lock 192 

Direct  Drive  Clutch 102 

Disc  Clutch  Calculating  Chart 41 

Disc  Clutch  Constructional  Details : 43 

Disc  Clutch  Data 38 

Disc  Clutch  Inner  Drum 44 

Disc  Clutch  Materials 38 

Disc  Clutch  Presser 45 

Disc    Clutch   Types 33 

Disc  Clutch,  Calculation  of 35 

Disc  Separating  Means 42 

Drive,  Double  Reduction 8 

Drive,  Single  Reduction 8 

Drop  Forged  Rear  Axle.  . . , 247 

Dux    Positive    Clutch    Gear 123 

Elliott  Type  Steering  Head 391 

Expanding  Clutch 62 

Fender  Brackets 493 

Fiat  Pressed  Steel  Axle 243 

Floating  Bushings 542 

Fluted  Shafts,  Tests  of 211 

Ford  Planetary  Gear 138 

Ford   Pressed   Steel   Axle 246 

Four  Wheel  Drives 5-351 

Frame  Cross  Members '. 480 

Frame  In-sweep 473 

Frame  Joints 482 

Frame  Materials 471 

Frame  Rail  Calculation 475 

Frame  Rails,  Bending  Moments  on 475 

Frame  Sections 479 

Frame  Sections,   Section  Moduli  of 480 

Frame  Steel  Gauge 471 

Frame  Trusses 485 

Frames,     Drop 473 

Frames,  Purpose   of 10 

Frames,  Underslung 483 

Frames,  Wood  Sill 484 

Friction  Clutch,    Purpose   of , 7 


566  INDEX. 

PAGE. 

Friction   Disc  and  Wheel,    Dimensions  of 153 

Friction   Disc   Drive,  Thrusts  and  Reactions  in 158 

Friction  Drive    Efficiency 151 

Friction    Drive,    Types    of 147 

Friction  Drive   Materials 150 

Friction   Lever   Control 443 

Friction  Wheel  and  Disc,  Engaging  Means  for 156 

Friction    Wheel    Applying    Mechanism 157 

Friction  Wheel   Sliding  Mechanism 155 

Friction,   Laws  of 38 

Friction,    Coefficients    of 15 

Front  Axle  Section  Diagram 389 

Front  Axles,   I-Section 388 

Front  Axles,   Manufacture   of 408 

Front  Axles,   Stresses   on 386 

Front  Axles,  Tubular  and  Pressed   Steel 408 

Front  Axles,  Weight  on 387 

Front   Mounted   Flywheel 199 

Front    Wheel    Bearings 397 

Front   Wheel   Bearings,   Mounting  of 399 

Front  Wheel  Drive 5 

Front  Wheel  Thrust  Loads 398 

Gear   Box   Lubrication 119 

Gear  Calculation  for  Strength 77 

Gear     Carrier 245 

Gear    Cases 115 

Gear   Material 72 

Gear  Motion,  Cause  of  Non-Uniform 215 

Gear  Reduction  Ratios 75 

Gear  Supporting  Methods 118 

Gear  Teeth,  Form  of 77 

Gear    Tester 110 

Geared-up  Fourth  Speed 114 

Governor  Control   Linkage 452 

Hele-Shaw   Clutch 46 

Helical  Bevel  Gears 215 

Hub  Caps 535 

Internal  Gear  Drive 348 

Jackshaft    340 

La  Buire  Arched  Axle 249 

Lamp  Brackets 495 

Lemoine  Type   Steering  Head 394 

Levassor    Sliding    Gear 70 

Locking  Device,  Ball  Wedge 443 

Maybach's    Selective   Gear 71 

Midland  Three  Point  Support 197 

Motor,  Location  of 3 

Panhard   Brake 376 

Pedal  Pads 456 

Pedals 453 

Pedals,    Adjustable 455 

Pedal   Shaft  Assembly 460 

Peerless  Arched  Axle 248 

Pitch   Line  Velocity 78 

Planetaries,  Calculation  of  All   Spur  Type 141 


INDEX.  567 

PAGE. 

Planetary,  All  Spur  Type 131 

Planetary,  Assembly  of  All   Spur  Type 136 

Planetary,  Assembly  of  Internal  Gear  Type 134 

Planetary,     Internal     Gear     Type 125 

Planetary  Gear,   Calculation  of  Speed  Ratios 126 

Planetary  Gear  Efficiency 145 

Planetary  Gears,  Bearing  Pressures  in 138 

Planetary  Gears,  Brakes  for 143 

Planetary  Gears,  Constructional  Details  of 143 

Planetary  Gears,  Gear  Stresses  in.  . 138 

Planetary  Pinions,  Required  Number  of  Teeth  in 130 

Plate  Clutch,  Dry 48 

Plate  Clutch,  Three 50 

Power  Plant,  Spring  Suspension  of 3 

Pressed  Steel  Rear  Axles 243 

Quadrants    467 

Quadrant  Designs,   Standard  S.  A.   E 468 

Quickest  Stop,  Conditions  Insuring  the 361 

Radiator   Brackets 490 

Radius  Rods,  Calculation  of 332 

Reach   Bar   or   Perch 10 

Rear  Axle  Bearing  Adjustment 257 

Rear  Axle  Bearing  Pressure 250 

Rear  Axle  Bearing  Housings 233 

Rear  Axle   Bearings 249 

Rear  Axle  Braces 277 

Rear  Axle  Thrust 265 

Rear    Axle    Thrust    Bearings 263 

Rear  Axle  Torsion 265 

Rear  Axle  Truss 264 

Rear  Axle,    Arched 247 

Rear  Axles,   Dead 338 

Rear  Axles,   Manufacture   of 288 

Rear  Axles,  Types  of 203 

Rear  Wheel  Drive 5 

Rebound    Clips 521 

Reverse    Gear   Arrangement 100 

Reverse    Lock-out 468 

Reversed  Elliott  Type  Steering  Head 393 

Roller  Chains,  Capacity  of 324 

Rudge-Whitworth    Wire   Wheel 538 

Schwarz  Interlocking  Spokes 536 

Seitz  Friction  Drive 148 

Semi-Floating  Axles,  Calculation  of   Shafts  for 213 

Shaft   Diameters,   Calculation   of 210 

Shaft   Joints 211 

Shaft    Materials 207 

Slider    Forks Ill 

Sliding  Gear  Efficiency 120 

Sliding   Gear   Locking   Dogs 112 

Sliding  Gear  Shaft  Front  Bearing. 102 

Sliding    Gear    Shaft 104 

Sliding  Gears,  Proportions  of 105 

Slip  Joints .  177 


568  INDEX 

PAGE. 

Spoke  Dimensions 532 

Spokes,     Number     of 531 

Spokes,  Proportions  of 531 

Sprags 384 

Spring     Arch 517 

Spring  Bolts 522 

Spring     Brackets 486 

Spring  Calculation,   Sample 511 

Spring  Centre  Bands 516 

Spring  Centre  Bolts 516 

Spring    Clips 518 

Spring  Eyes 522 

Spring  Leaf  Points 523 

Spring  Leaves,  Alignment  of 522 

Spring    Leaves,    Reverse 521 

Spring   Lengths   and    Widths,   Table    of 505 

Spring     Lips 522 

Spring    Lubrication 526 

Spring    Material 500 

Spring    Perches 518 

Spring    Plates,    Number   and    Thickness    of 510 

Spring  Play  on  Bevel  Gear  Drive,  Effect  of 270 

Spring  Play   on   Chain  Drive,  Effect  of 334 

Spring  Pressure  Blocks 520 

Spring  Shackles 522 

Spring  Steel  Gauge 507 

Springs,    Auxiliary . 526 

Springs,   Cantilever 499 

Springs,     Eccentrated 509 

Springs,   Flexibility  of 507 

Springs,     Inclined 524 

Springs,    Theory    of   Leaf 501 

Springs,  Torsion   and   Thrust   on 525 

Springs,  Total  Deflection  Constants  of L 508 

Springs,  Types  of    497 

Sprocket   Wheels,    Design    of 326 

Sprockets,     Overhanging 328 

Starting   Crank   Bracket 494 

Steering  Angles,   Chart   of 418 

Steering  Arm 432 

Steering    Column 438 

Steering    Column,    Adj  ustable 439 

Steering   Connectors 433 

Steering  Drag  Link 433 

Steering,    Four   Wheel 5 

Steering,  Front 4 

Steering,   Rear 4 

Steering    Gear    Bearings 424 

Steering  Gear,  Calculation  of  Worm  and  Wheel 420 

Steering   Gear    Cases    426 

Steering   Gear,    History   of .' 411 

Steering  Gear,   Support  of 431 

Steering  Gears,  Double  Screw  Adjustable 429 

Steering   Gears,    General   Arrangement   of 418 


INDEX  569 

PAGE. 

Steering  Gears,  Reversible  and   Non-Reve'rsible 419 

Steering  Gears,  Screw  and  Nut  Type 428 

Steering   Heads    390 

Steering    Knuckle   Arms    403 

Steering  Mechanism,   Bevel   Gear .  430 

Steering  Mechanism,  Theory  of 411 

Steerings   Pivot    Bearings,    Calculation    of 394 

Steering  Pivot,  Inclined 396 

Steering  Problem,   Analytic   Solution   of 415 

Steering    Problem,    Graphical    Solution    of 412 

Steering   Shaft    424 

Steering  Spindle   Diameter 402 

Steering  Stops    402 

Steering    Spindle    "Set". . . , 401 

Steering  Tie  Rod    405 

Steering  Tie   Rod   Connectors 407 

Steering   Wheel 435 

Step      Hangers 494 

Straight  Line  Drive    202 

Stub  Tooth    77 

Sub     Frames     481 

Swiveled    Gear    Box 201 

Three   Point    Support 195 

Throttle    Linkage     451 

Timken    Brake    377 

Timken  Pressed   Steel  Axle   244 

Torque   Rod    Supports    276 

Torque    Rods    274 

Torque    Tubes 266 

Torque   Tube    Supports    268 

Trailer   Steering  Axle    396 

Transmission   Axles    199 

Transmission    Brakes    367 

Tread    10 

Truck    Bumpers     491 

Unit  Power  Plants   193 

Universal  Joint,  Anti-Friction   Bearing    176 

Universal  Joint,  Calculation  of  Block  and  Trunnion  Type 173 

Universal  Joint,  Calculation   of   Forked  Type 169 

Universal  Joint,  Dust   Protection   of    174 

Universal  Joint,  Lubrication    of    174 

Universal  Joint  Sheet  Metal  Housing 175 

Universal  Joint,   Square  Block  Type 168 

Universal  Joints,    Leather    Disc   Type 177 

Universal  Joints,  Proper  Angular  Relation  of  Double   168 

Universal  Joints,  Speed  Fluctuations  in   163 

Universal  Joints,  Types  of   160 

Weights  of  Commercial  Cars    387 

Wheel   Base    ....*..*.  10 

Wheel  Bearings   258 

Wheel  Bearings,  Mounting  of 260 

Wheel    Diameters    '  cog 

Wheel  Hubs   '                                        '  S33 

Wheel    Material,  'Wood '.'. ... '.  '. '. '. ..............                  [  S28 


570  INDEX 

PAGE. 

Wheels,   Artillery    528 

Wheels,  Cast  Steel    540 

Wheels,    Manufacture    of 53/ 

Wheels,   Number  of    4 

Wheels,    Wire    537 

Worm  Driven  Axle  Design    316 

Worm  Drive,  Advantages  of 293 

Worm  Drive,   History   of    293 

Worm  Drive  Axle  Tube  Dimensions,   Calculation  of 318 

Worm  Gear  Efficiency    298 

Worm  Gear  Efficiency  Tests    305 

Worm    Gear    Formulae,    Application    of 309 

Worm    Gear,   Hindley  Type 312 

Worm  Gear   Housings    316 

Worm  Gear  Load   Capacity,  Calculation   of 302 

Worm  Gear  Material    310 

Worm  Gear   Radial    Bearing   Loads 301 

Worm  Gear  Thrust   Bearing  Loads 300 

Worm  Gearing,  Theory  of    294 

Worm  Gears,  Axial  Pitch  of 296 

Worm  Gears,  Centre  Distance  of   302 

Worm  Gears,   Pressure  Angle  of    295 

Worm,  Mounting    of    315 

Worm  Top  Mounted  and  Bottom  Mounted 314 

Worms,  Hardening  and  Polishing  of   310 


PLATE  SUPPLEMENT. 


CHANGE  SPEED  GEAR  OF  THE  PACKARD  TWELVE. 


571 


PLATE  SUPPLEMENT. 


DRY  Disc  CLUTCH  OF  CHALMERS  6-30. 


PLATE  SUPPLEMENT. 


573 


BROWN-LIPE  DRY  Disc  CLUTCH 
ON   CUNNINGHAM    CAR. 


574 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


575 


576 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


577 


578 


PLATE  SUPPLEMENT. 


BORG  &  BECK  PLATE  CLUTCH  AND  COVERT  CHANGE  GEAR. 


PLATE  SUPPLEMENT. 


579 


TIM  KEN  TRUCK  FRONT  AXLE  (7,200  LBS.  MAX.  LOAD), 


580 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


581 


582 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


585 


586 


PLATE  SUPPLEMENT. 


FRANKLIN  STEERING  GEAR. 


PLATE  SUPPLEMENT. 


587 


BENZ  STEERING  GEAR. 


588 


PLATE  SUPPLEMENT. 


PEERLESS  TRUCK  STEERING  GEAR. 


PLATE  SUPPLEMENT. 


590 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


591 


PLATE  SUPPLEMENT. 

;•— ' 

o 


PLATE  SUPPLEMENT. 


593 


594 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


595 


596 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


597 


tn 

i 

I 

u 

S 

o 
fc 

U 

H 

S 
o 

W 


598 


PLATE  SUPPLEMENT. 


PLATE  SUPPLEMENT. 


599 


600 


PLATE  SUPPLEMENT. 


»B 


PLATE  SUPPLEMENT. 


601 


u 


602 


PLATE  SUPPLEMENT. 


~/)   /I    r    . 
U-f 


RETURN     CIRCULATION  DEPARTMENT 

202  Main  Library 


LOAN  PERIOD  1 
HOME  USE 

2 

3 

4 

5 

6 

AJl  BOOKS  MAY..BE  RECALLED  AFTER  7  DAYS 


DUE  AS  STAMPED  BELOW 


AUG  12  1990 


jUL  ^  ^  199 


UNIVERSITY  OF  CALIFORNIA,  BERKELEY 

FORM  NO.  DD6,  60m,  1  /83          BERKELEY,  CA  94720 

®$ 


GENERAL  LIBRARY  -  U.C.  BERKELEY 


BDOD35277b 


